a skier (50kg) starts at 3m/s at top of a hill 85 m high. what is her final speed? final kinetic energy?

Answer 1

1d = Vot + 1/2 gt²
85 = 3t + 1/2*9.8 t²
4.9t² + 3t - 85 = 0
t = 3.87 or -4.48 (no time is -ve)
so
t = 3.87 S
V = Vo + gt
v = 3 + 3.87*9.8
v = 40.926 m/s

KE = 1/2 mv²
= 1/2 * 50 * 40.926²
= 41873.44J
=41.87 KJ

Answer 2

Let's find the skier's potential energy first. Potential energy is given by PE = mgh. So in this case, the skier's potential energy is

PE = (50 kg) * (9.8 m/s^2) * (85 m) = 41650 J.

In addition, the skier has an initial velocity of 3 m/s. Kinetic energy is KE = (1/2)mv^2, so the skier's initial kinetic energy is

KE = (1/2)(50 kg) * (3 m/s)^2 = 225 J.

When the skier is at the bottom of the hill, all the potential energy will have been used up and converted to kinetic energy, so the final kinetic energy will be

KE = 225 J + 41650 J = 41875 J.

Now we can find the velocity using the kinetic energy equation:

KE = (1/2)mv^2
41875 J = (1/2)(50 kg)v^2
1675 m^2/s^2 = v^2
40.92 m/s = v.

So the skier's final velocity is about 41 m/s.