Mechanics | Relativity Answers

Q2. The altitude of a rocket in the first half-minute of its ascent is given by x = bt2, where x is the altitude and b = 2.90 m/s2 is a constant.
a) Find a general expression for the rocket’s velocity as a function of time.
b) Find the rocket’s instantaneous velocity at t = 20 s.
c) Find an expression for the average velocity of the rocket. Find the average velocity after during the first 20 seconds.
d) Compare your two velocities (instantaneous and average). Is there a difference and if so why?

Q1. A speeding motorist zooms through a 50 km/h zone without noticing a stationary police car. The police officer immediately heads after the speeder, accelerating at 2.5 m/s2 (i.e. the speeder and the cop start at the same starting point). The officer catches up to the speeder 350 m down the road (i.e. the speeder and the cop arrive at the same point 350 m from where the speeder first passes the cop).
Assuming that the speeder is going at a constant speed, answer the following:
a) Sketch three motion graphs of the situation: the acceleration chart, the velocity chart and the position chart. Please put both the lines describing the speeder and the officer’s motion on the same chart and label the lines using “cop” and “speeder” and the equation of the lines.

b) Give the general expression for the position of the police officer with respect to time. How long does it take the police officer to catch up to the speeder (seconds)?

c) Give the general expression for the position of the speeder with respect to time. Given the information you know what is the velocity of the speeder (km/h)? Was the speeder breaking the speed limit?
d) Give the general equation for the velocity of the police officer? How fast is the police officer going when he catches up to the speeder (km/h)?

Three rods of the same mass are placed like a triangle.What will be the coordinate of centre of mass of the system?

harry accidentally falls out of a helicopter that is traveling at 15 m/s. he plunges into a swimming pool 2 seconds later. assuming no air resistance, what was the horizontal distance of between Harry and the swimming pool when he fell from the helicopter

A golfer is tryinh to improve the range of her shot. To do so she drives a golf ball from the top of a steer cliff 30.0m above the ground where the ball will land. If the ball has an initial velocity of 25m/s and is launched at an angle at an angle of 50 degree above the horizontal, determine the ball's time of flight,its range, and its final just before it hits the ground

a bullet with a mass of 50 gr and a velocity of 200m/s is stopped by a wall. How much has the internal energy of the bullet and the wall have increased

difference between height and altitude

A bullet moving with a speed 'v' can just penetrate two planks of equal thickness. Find the number of such planks that the bullet will penetrate if its speed is doubled.

A company has asked you to design a new Gravitron ride. They have a motor that will spin the passengers at 28m/s and would like to know how large the machine needs to be in order for the passengers to feel 8g's of acceleration.

The Gravitron is a circular carnival ride that is 6.2m in radius and spins at a high rate of speed in order to simulate gravity. What velocity is required to experience an acceleration equal to Earth's gravity (aka 1g)?

If the velocity were 2 times faster, how many g's would the riders feel?

How would the radius need to change to allow the riders to experience 5g's at this new velocity?