Question

A 1500 kg rocket is launched straight up. If the initial velocity of the rocket is 25 m/s, how fast is the rocket going when it reaches a height of 26 m. Ignore air resistance.

Answer 1

Kinetic energy=1/2mv2, where m is mass and v is velocity.

Gravitational potential energy = mgh , where m is mass, g is gravitational acceleration and h is height.

Here,m=1500 kg.

Now, initially, h=0. So, gravitational potential energy = 0 J.

Also, initially, v = 25 m/s. So, initial kinetic energy = 1/2*1500*25*25 = 468750 J.

So, initial energy = 468750+0 = 468750 J.

Finally, h = 26 m. So, final potential energy = 1500*9.8*26 = 382200 J.

Let final velocity be u. So, final kinetic energy = 1/2*1500*u*u = 750*u*u.

So,final energy = 750u*u+382200

Now, final energy = initial energy

=>750u*u+382200 = 468750

=>750*u*u = 468750 - 382200 = 86550

=>u*u = 86550/750 = 115.4

=>u=10.74 m/s.

So, required final velocity = 10.74 m/s.