# free falling problem

• Sep 13th 2008, 10:37 PM
yzc717
2 free falling problems (1 remains)
1.
Quote:

A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 2.00 m.

(a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move?

(b) How long is he in the air?

2.
Quote:

A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 79.8 m/s at ground level. Its engines then fire and it accelerates upward at 3.80 m/s2 until it reaches an altitude of 1130 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of -9.80 m/s2. (You will need to consider the motion while the engine is operating separate from the free-fall motion.)

(a) How long is the rocket in motion above the ground?

(b) What is its maximum altitude?
km

(c) What is its velocity just before it collides with the Earth?
• Sep 13th 2008, 11:38 PM
mr fantastic
Quote:

Originally Posted by yzc717
1.
Quote:
A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 2.00 m.

(a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move?

(b) How long is he in the air?

Ranch hand:

a = g = 9.8 m/s^2
u = 0 m/s
x = 2 m
t = ?

Using $\displaystyle x = ut + \frac{1}{2} a t^2$: $\displaystyle 2 = 4.9 t^2 \Rightarrow t = 0.64$ seconds.

Horse: x = 10t

Substitute t = 0.64: x = 6.4 metres.