Question

1 A ball is dropped from 20.0 ft above the ground. Using energy considerations only, what is the velocity (in ft/s) of the ball just as it hits the ground? Enter answer 2 What is the velocity (in m/s) of a 55.0 kg jogger with a kinetic energy of 1,380.0 J? Enter answer 3. A small sports car and a pickup truck start coasting down a 35.0 m hill together, side by side Assuming no friction, what is the velocity (in m/s) of both vehicles at the bottom of the hill? Enter answer 4. A 65.0 kg student runs up the stairs of a football stadium to a height of 15.0 m above the ground in 10.0 s. What is the power of the student in kw? Enter answer The potential energy of a 15.0 kg ball is 2,420 J while at rest. If the ball is released, how fast will it be moving in m/s when it strikes the ground? Enter answer

Answer 1

1.

$mgh=\frac {1}{2}mv^2$  

$v=\sqrt {2gh}$

$v=\sqrt {2\cdot 32.2\cdot 20}\: ft/s= 35.88\: ft/s$

2.

$\frac {1}{2}mv^2=1380\: J$

$\frac {1}{2}\cdot 55v^2=1380\: J$

$v=7.084\: m/s$

3.

$v=\sqrt {2gh}$

$v=\sqrt {2\cdot 9.8\cdot 35}\: m/s=26.19\: m/s$

4.

$P=\frac {W}{t}=\frac{mgh}{t}=\frac {65\cdot 9.8\cdot 15}{10}\:W= 0.955\: W$

5.

$h=\frac {P}{mg}=\frac {2420}{15\cdot 9.8}\: m= 16.46\: m$

$v=\sqrt {2gh}=\sqrt {2\cdot 9.8\cdot 16.46}\: m/s= 17.96\: m/s$