Answer to Question #263952 in Mechanics | Relativity for Laxus

Question

1. If an arrow is fired from a bow with a perfectly horizontal velocity of 60.0 m/s and the arrow was 2.00 m above the ground when the it was released, how far will the arrow fly horizontally before it strikes theground?

2. A rock was thrown horizontally from a 100.0 m high cliff. It strikes the ground 90.0 m from the base of the cliff. At what speed was it thrown?

3. A cliff diver running 3.60 m/s dives out horizontally from the edge of a vertical cliff and reaches the water below 2.00 s later. How high is the cliff and how far from the base of the cliff did the diver hit the water?

4. During a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of75.0º above the horizontal. The fuse is timed to ignite the shell just as it reaches its highest point above the ground.

a. Calculate the height at which the shell explodes.

b. How much time passed between the launch of the shell and the explosion?

c. What is the horizontal displacement of the shell when it explodes?

Answer 1

1)

$t=\sqrt{\frac{2h}g}=0.63~s,$

$l=vt=38~m.$

2)

$t=\sqrt{\frac{2h}g}=4.47~s,$

$v=\frac lt=20~\frac ms.$

3)

$h=\frac{gt^2}2=20~m,$

$l=vt=7.2~m.$

4)

a)

$h=\frac{v^2\sin^2\alpha}{2g}=229~m,$

b)

$t=\frac{v\sin\alpha}g=6.8~s,$

c)

$l=vt\cos\alpha=123~m.$