Question

Sam, whose mass is 75 kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 160 N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 15 s .

A: What is Sam's top speed?

- I found the answer to be 17 m/s (can you check this for me?)

B: How far has Sam traveled when he finally coasts to a stop? (I have no idea for this one)

PLEASE HELP. AND I ONLY HAVE ONE SHOT TO PLEASE ONLY ANSWER IF YOU TURLY KNOW

Answer 1

Concepts and reason

The required concepts to solve the problem are kinematic equations and Newton’s laws of motion.

First, using Newton’s second law, find the acceleration and then using kinematic equation of motion, find the top speed of Sam. Then, find the distance travelled when there was fuel and then find the distance travelled when the fuel was empty and add the distance to find the total distance travelled by Sam.

Fundamentals

According to Newton’s second law, the force applied to a body is proportional to the acceleration of the body.

The Newton’s second law can be written as,

$F=ma $

Here, is the force, is the mass andis the acceleration.

The expression for the frictional force is,

Here, f is the frictional force, is the coefficient of friction, and g is the acceleration due to gravity.

The kinematic equations of motion are,

Here, is the initial velocity, is the final velocity, is the acceleration, is the time andis the distance travelled.

(A)

From Newton’s second law, the acceleration of the body is,

Use for f.

Substitute for , for , for and for .

The kinematic equation of motion is,

Substitute for , for and for .

(B)

The initial distance travelled is,

Substitute for , for and for .

The expression for Sam’s acceleration after is,

Use for f.

Substitute for and for .

Acceleration is actually negative because the speed is decreasing.

The equation of motion is,

Rewrite the above equation for the time taken Sam to come to rest.

Substitute for , for and for .

The distance travelled is,

Substituteforandfor.

The total distance traveled by Sam is,

$d=s+s $

Substituteforandfor.

Ans: Part A

The top speed of Sam is .