**
Projectile**

Physics requires practice to develop your solving problems
skills and your logical thinking . I strongly recommend to study carefully the
examples, and solve the following problems *in your
book.*

Examples: 3.4 - 3.9 Pages. 57 - 61

Problems: 17, 19, 21, 23, 25, 27, 29, 30, 31, 33, 37, 39, 41, 43, 47 Pages. 66 - 68

Problems for Teaching

1. (17G)**
**A tiger leaps horizontally from a 6.5-m-high rock with a speed
of How
far from the base of the rock will she land?

2. (18G) A diver running dives out horizontally from the edge of a vertical cliff and 3.0 s later reaches the water below. How high was the cliff, and how far from its base did the diver hit the water?

3. (12S) In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor 1.4o m from the base of the counter. If the height of the counter is 0.860 m, a) with what velocity did the mug leave the counter, and b) what was the direction of the mug's velocity before it hits the floor?

4. (19G) A fire hose held near the ground shoots water at a speed of At what angle(s) should the nozzle point in order that the water land 2.0 m away (Fig. 3–33)? Why are there two different angles? Sketch the two trajectories.

5. (21G) A ball is thrown horizontally from the roof of a building 45.0 m tall and lands 24.0 m from the base. What was the ball’s initial speed?

6. (22G) A football is kicked at ground level with a speed of at an angle of 35.0º to the horizontal. How much later does it hit the ground?

7. (23G) A ball thrown horizontally at from the roof of a building lands 36.0 m from the base of the building. How tall is the building?

8. (25G) Determine how much farther a person can jump on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.

9. (27G) The pilot of an airplane traveling wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?

10.
(30G) A projectile is fired with an initial speed of at
an angle of 34.5º above the horizontal on a long flat firing range. Determine (*a*)
the maximum height reached by the projectile, (*b*) the total time in the
air, (*c*) the total horizontal distance covered (that is, the range), and
(*d*) the velocity of the projectile 1.50 s after firing.

11.
(31G)
A projectile is shot from the edge of a cliff 125 m above ground level with an
initial speed of at
an angle of 37.0º with the horizontal, as shown in Fig. 3–35. (*a*)
Determine the time taken by the projectile to hit point P at ground level. (*b*)
Determine the range *X* of the projectile as measured from the base of the
cliff. At the instant just before the projectile hits point P, find (*c*)
the horizontal and the vertical components of its velocity, (*d*) the
magnitude of the velocity, and (*e*) the angle made by the velocity vector
with the horizontal. (f) Find the maximum height above the cliff top reached by
the projectile.

12.
(33G**)**
At what projection angle will the range of a projectile equal its maximum
height?

13.
(35G)
A rescue plane wants to drop supplies to isolated mountain
climbers on a rocky ridge 235 m below. If the plane is traveling horizontally
with a speed of (*a*)
how far in advance of the recipients (horizontal distance) must the goods be
dropped (Fig. 3–37a)? (*b*) Suppose, instead, that the plane releases the
supplies a horizontal distance of 425 m in advance of the mountain climbers.
What vertical velocity (up or down) should the supplies be given so that they
arrive precisely at the climbers’ position (Fig. 3–37b)? (*c*) With what
speed do the supplies land in the latter case?

14. (10S) To start an avalanche on a
mountain slope, an artillery shell is fired with an initial velocity of 300 m/s
at 55.0° above the horizontal. It explodes on the mountainside 42.0 s after
firing. What are the *x* and *y* coordinates of the shell where it
explodes, relative to its firing point?

15.
(13S)** **One strategy in
a snowball fight is to throw a snowball at a high angle over level ground.
While your opponent is watching the first one, a second snowball is thrown at a
low angle timed to arrive before or at the same time as the first one. Assume
both snowballs are thrown with a speed of 25.0 m/s. The first one is thrown at
an angle of 70.0° with respect to the
horizontal. (a) At what angle should the second snowball be thrown to arrive at
the same point as the first? (b) How many seconds later should the second
snowball be thrown after the first to arrive at the same time?

16. (14S)** **An astronaut on a strange
planet finds that she can jump a maximum horizontal distance of 15.0 m if her
initial speed is 3.00 m/s. What is the free-fall acceleration on the planet?

17. (15S) A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?

18. (19S) A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0° to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling?

** **

19. (21S) A playground is on the flat roof of a city school, 6.00 m above the street below. The vertical wall of the building is 7.00 m high, to form a meter-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of 53.0° above the horizontal at a point 24.0 meters from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (a) Find the speed at which the ball was launched. (b) Find the vertical distance by which the ball clears the wall. (c) Find the distance from the wall to the point on the roof where the ball lands.

20.
(54S)** **A basketball player who is
2.00 m tall is standing on the floor 10.0 m from the basket, as in Figure
P4.54. If he shoots the ball at a 40.0°
angle with the horizontal, at what initial speed must he throw so that it goes
through the hoop without striking the backboard? The basket height is 3.05 m.

** **

21 (19E) A plane is flying due north at 325 km/h. Suddenly there is a wind from the south at 45 km/h. What is the plane’s new velocity with respect to the ground in standard position?

22. (21E) A plane is flying due west at 235 km/h. Suddenly there is a wind from the north at 45.0 km/h. What is the plane’s new velocity with respect to the ground in standard position?

23. (24E) A plane is flying southeast at 215 Km/h. Suddenly there is a wind from the north at 75.0 km/h. What is the plane’s new velocity with respect to the ground in standard position?