# Worksheet: Projectile Motion

In this worksheet, we will practice how to use parametric equation properties to describe a projectileβs motion in x- and y-directions as a function of time.

Q1:

A particle projected with a velocity m/s from a fixed point in a horizontal plane landed at a point in the same plane 360 m away. Find the value of and the projectileβs pathβs greatest height . Take .

• A ,
• B ,
• C ,
• D ,
• E ,

Q2:

A particle projected from the origin passed horizontally through a point with a position vector of m, where and are horizontal and vertical unit vectors respectively. Determine the velocity with which the particle left , considering the acceleration due to gravity to be 9.8 m/s2.

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q3:

A particle started moving from with a velocity of m/s, where and are unit vectors horizontally and vertically upwards respectively. Find, giving your answer to the nearest integer, the distance of the particle from after 1 s. Consider the acceleration due to gravity to be 9.8 m/s2.

Q4:

If a particle was projected from the origin on a horizontal ground with initial velocity m/s, write its position vector at time seconds. Consider the acceleration due to gravity to be 9.8 m/s2.

• A m
• B m
• C m
• D m
• E m

Q5:

A particle was projected from a point with a position vector m relative to the origin . After 2 seconds, it was at a point m relative to , where and are the horizontal and vertical unit vectors respectively. Calculate the distance of the particle from after a further 5 seconds. Take the acceleration due to gravity to be 9.8 m/s2.

Q6:

A particle of mass 0.7 kg is attached to end of a light rod of length 0.7 m. The rod is free to rotate in a vertical plane about . The particle is held at rest with at to the upward vertical. The particle is released. Calculate the tension in the rod as the particle passes through the lowest point of the path, giving your answer to the nearest two decimal places. Consider the acceleration due to gravity to be 9.8 m/s2.

Q7:

A smooth solid hemisphere has its flat surface lying on a horizontal table and its curved surface facing upwards. The flat face of the hemisphere has centre and radius . Point , at which a particle is placed, is the highest point on the hemisphere. is then given an initial horizontal speed , where and the acceleration due to gravity is . Find the angle at which strikes the table to the nearest degree.