Question

A 0.23 kg object experiences air resistance when it falls 17 m to the ground. It hits the ground with a speed of 13 m/s. How fast would the stone have landed if there had been no air resistance?

Answer 1

We can use the equation for gravitational potential energy to find the initial velocity of the object if there had been no air resistance:

mgh = (1/2)mv^2

where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), h is the height it falls, and v is the final velocity.

Plugging in the given values, we get:

(0.23 kg)(9.8 m/s^2)(17 m) = (1/2)(0.23 kg)v^2

Solving for v, we get:

v = sqrt[(2 x 0.23 kg x 9.8 m/s^2 x 17 m)/0.23 kg]
= sqrt[2 x 9.8 m/s^2 x 17 m]
= 16.1 m/s

Therefore, the object would have landed with a speed of 16.1 m/s if there had been no air resistance.