Answer to Question #135953 in Physics for ffvfd

Question

2. Sanna rolls a ball up to another person on a smooth ramp 19.6 m above her. The ball reaches the other person’s hands when it is travelling 4.9 m/s uphill. If the ramp angle slows the ball down by 3.7 m/s each second it travels up the ramp, find the initial velocity of the ball.

Answer 1

According to energy conservation principle, the initial kinetic energy was wasted to increase height of the ball and some rest kinetic energy left:

$$\frac{mv_i^2}{2}=\frac{mv_f^2}{2}+mgh,\\\space\\ \frac{v_i^2}{2}=\frac{v_f^2}{2}+gh,\\\space\\ \frac{v_i^2}{2}=\frac{4.9^2}{2}+9.8\cdot19.6,\\\space\\ v_i=20.2\text{ m/s}.$$