Question

A young child uses a slingshot to launch a rock straight up at a speed of 12 m/s and then catches it at the point from where he launched it. What is the maximum height that the rock reaches?

A. 7.2 m
B. 14.4 m
C. 28.8 m
D. None of the above

Answer 1

Using the kinematic equation for projectile motion, the maximum height reached by the rock launched vertically at 12 m/s is calculated to be approximately 7.3 m, which is not an option provided in the multiple-choice answers. Therefore, the answer is D. None of the above.

Step-by-step explanation:

To calculate the maximum height reached by a rock launched from a slingshot going straight up, we use the kinematic equation that relates initial velocity, acceleration due to gravity, and the maximum height (final velocity at the peak is zero). The equation is:

v2 = u2 + 2gh

where:

• v is the final velocity (0 m/s at the highest point),
• u is the initial velocity (12 m/s),
• g is the acceleration due to gravity (9.8 m/s2, which is negative in this case as it is acting downward),
• h is the maximum height (what we are solving for).

Rearranging and solving for h gives us:

h = - u2 / (2g)

Substituting the values:

h = - (12 m/s)2 / (2 (-9.8 m/s2))

h = 144 / 19.6

h = 7.34694 m

The maximum height to the nearest tenth is 7.3 m, which is not listed in the provided multiple-choice answers, so the correct answer is D. None of the above.