Lesson Worksheet: Projectile Motion Formulae Mathematics

In this worksheet, we will practice deriving formulae for projectile motion and using them in problems.

Q1:

A projectile is launched from a flat horizontal plane at an angle of from the horizontal. Its initial velocity is m/s, its acceleration due to gravity is m/s2, and no other forces act upon it during its flight. Given that its time of flight is s, find the value of the constant .

• A2
• B1
• C4
• D
• E

Q2:

A projectile is launched from a flat horizontal plane at an angle of from the horizontal. Its initial velocity is m⋅s−1, its acceleration due to gravity is m⋅s−2, and no other forces act upon it during its flight. Given that its range on the horizontal plane is , find the value of the constants and .

• A,
• B,
• C,
• D,
• E,

Q3:

A projectile is launched from a flat horizontal plane at an angle of from the horizontal. Its initial velocity is ms−1, its acceleration due to gravity is ms−2, and no other forces act upon it during its flight. Given that its greatest height is , find the value of the constants , , and .

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q4:

A projectile is launched from a flat horizontal plane at an angle of from the horizontal. Its initial velocity is ms−1, its acceleration due to gravity is ms−1, and no other forces act upon it during its flight. Derive an equation relating its vertical displacement to its horizontal displacement at any given time.

• A
• B
• C
• D
• E

Q5:

A particle is projected from a horizontal plane at an angle of from the horizontal. After 15 seconds, the particle hits the ground. Find the starting velocity of the particle, taking and giving your answer to 1 decimal place.

Q6:

A projectile is launched from a flat horizontal plane at an angle of from the horizontal. Its initial velocity is m/s, its acceleration due to gravity is m/s2, and no other forces act upon it during its flight. Given that its range on the horizontal plane is m, find the value of that maximizes .

• A
• B
• C
• D
• E

Q7:

A particle is projected from a horizontal plane at an angle of from the horizontal. It reaches its greatest height after 2 seconds. Find the starting velocity of the particle, taking and giving your answer to 1 decimal place.

Q8:

A particle is projected from a horizontal plane at an angle of from the horizontal and with an initial velocity of 18 m/s. The particle passes through point situated 15 m horizontally and 8 m vertically from the point of launch. Find the possible values of , taking and giving your answer to 1 decimal place.

• A or
• B or
• C or
• D or
• E or

Q9:

A rocket is launched vertically at a speed of 60 m/s from a point . When it reaches its maximum height, a capsule is ejected horizontally from it at a speed of 40 m/s. Find the horizontal distance from to the capsule’s landing point, taking and giving your answer to 1 decimal place.

Q10:

A projectile is launched from a flat horizontal plane with an initial velocity of m/s, where and are unit vectors in the horizontal and vertical directions. Its acceleration due to gravity is m/s2, and no other forces act upon it during its flight. Given that its position vector relative to the origin is with and related by , find the values of the constants and .

• A,
• B,
• C,
• D,
• E,

This lesson includes 45 additional question variations for subscribers.