Answer to Question #319068 in Mechanics | Relativity for Joshua

Question

Answer the following with full solution.

1.) A stone is thrown vertically up from the ground with a velocity of 400 ft per sec. How long must one wait before dropping a second stone from the top of an 800ft tower if the two stones are to pass each other 300 ft from the top of the tower?

2.) It was once recorded that a Jaguar left skid marks that were 290 m in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of -3.90 m/s², determine the speed of the Jaguar before it began to skid.

3.) A capsule orbit the earth at the rate of 6000 m/s. If the radius of the Earth is 3000km, find the height of capsule from the surface of the Earth.

Answer 1

1.

$t_1=\frac vg=24.9~s,$

$h_m=\frac{v^2}{2g}=2486~ft,$

$300=\frac g2(t-t_2)^2,$

$1986=\frac g2t^2,$

$t_2=\sqrt{\frac{2\cdot 1986}g}-\sqrt{\frac{2\cdot 300}g}=6.8~s,$

$t=t_1+t_2=31.7~s,$

2.

$v=\sqrt{2as}=47.6~\frac ms,$

3.

$v=\sqrt{\frac{gR^2}{R+h}},$

$h=\frac{gR^2}{v^2}-R=4750~km.$