A rock climber throws a small first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 5.70 m/s at an angle of 45.7 ° above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero. What is the vertical height between the two climbers?

Height difference between climbers = 0.85 m.

Explanation:

Vertical motion of first aid kit:

Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s

Acceleration, g = - 9.81 m/s²

When the climber who is higher up the mountain catches the kit it's vertical speed is zero.

Final vertical velocity, v = 0 m/s

We have equation of motion, v² = u² + 2as

Substituting

0² = 4.08² + 2 x - 9.81 x s

s = 0.85 m

So the kit travels 0.85 m vertically.

Height difference between climbers = 0.85 m.