This lesson includes 45 additional question variations for subscribers.

# 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/s^{2},
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 mβ
s^{β1},
its acceleration due to gravity is mβ
s^{β2},
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^{β1},
its acceleration due to gravity is
ms^{β2},
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^{β1},
its acceleration due to gravity is ms^{β1},
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/s^{2}, 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 capsuleβs 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/s^{2}, 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,