Question

A physics student rolls a ball down a hill with an initial velocity of 2.5m/s. If it accelerates down the hill at a rate of 6.3m/s^2, How long will it take to reach the bottom of the hill, 150 meters away?

Please help!!!

Answer 1

I'll assume you mean the hill is 150 m along its slope, since that's the direction the ball rolls.

The distance x it rolls after time t is

x = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

Set x = 150 m and solve for t :

150 m = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

(3.15 m/s²) t² + (2.5 m/s) t - 150 m = 0

t = 1/2 [(-2.5 m/s) + √((2.5 m/s)² - 4 * (3.15 m/s²) * (-150 m))]

(Use the quadratic formula, and take the positive root)

t ≈ 6.52 s