Question

A boy uses a slingshot to launch a pebble straight up into the air. The pebble reaches a height of 37.0 m above the launch point 2.3 seconds later. Assume air resistance is negligible (a) What was the pebble's initial speed (just after leaving the slingshot)? m/s (b) How much time did it take for the pebble to first reach a height of 18.5 m above its launch point? s

Answer 1

The pebble's initial speed is approximately 22 m/s. It takes approximately 1.45 seconds for the pebble to first reach a height of 18.5 m.

Step-by-step explanation:

To determine the pebble's initial speed, we can use the equation for projectile motion:

h = v0yt - (1/2)gt2

Where h is the height, v0y is the initial vertical speed, t is the time, and g is the acceleration due to gravity.

Since the pebble is launched straight up, the final height is equal to the initial height. Plugging in the given values, we have:

37 m = v0y(2.3 s) - (1/2)(9.8 m/s2)(2.3 s)2

Simplifying this equation gives us the value of v0y, the initial vertical speed. To find the pebble's initial speed, we can use the Pythagorean theorem:

v0 = √(v0x2 + v0y2)

Where v0 is the initial speed and v0x is the initial horizontal speed. Since the pebble is launched straight up, v0x = 0. Plugging in the calculated value of v0y, we can solve for v0.

(a) The pebble's initial speed is approximately 22 m/s.

(b) To find the time it takes for the pebble to first reach a height of 18.5 m, we can use the equation for height:

18.5 m = v0yt - (1/2)gt2

Solving for t gives the time it takes for the pebble to reach the desired height.

(b) It takes approximately 1.45 seconds for the pebble to first reach a height of 18.5 m.