Question

1) A 783 kg coupe is traveling at 26.0 m/s when the driver wishes to come to a stop. When he pushes down on the brake pedal, a braking force of 2890 N acts on the coupe to slow it down. How long, in seconds, will it take to come to a stop? Round your answer to the nearest hundredth

2) A 56 kg skateboarder stands at rest on the lip on one side of a half-pipe. She then rolls down that side, picking up speed until she reaches 6.8 m/s at the bottom. In meters, how tall must the side of the half-pipe be to give her that speed at the bottom? Round your answer to the nearest tenth..

Please solve both the question. Will rate the answer for sure. Thanks

Answer 1

1)
The initial velocity of the car, u = 26.0 m/s
Acceleration of the car, a = - F/m
Where F is the braking force and m is the mass. Acceleration is negative since the car is slowing down.
a = - 2890 / 783
= - 3.69 m/s²
The final velocity of the car, v = 0
Consider t as the time taken.

Using the formula, v = u + a * t,
t = (v - u) / a
= (0 - 26) / (- 3.69)
= 7.04 s

2)
The initial energy of the skateboarder, Ei = m * g * h
Where m is the mass of the skateboarder and h is the height of the half-pipe

Final energy of the skateboarder, Ef = 1/2 * m * v²
Where v is the velocity of the skateboarder at the bottom.

Using conservation of energy, Ei = Ef
m * g * h = 0.5 * m * v²
h = v² / 2g
= 6.8² / (2 * 9.8)
= 2.4 m