# Lesson Worksheet: Impulse and Momentum Mathematics

In this worksheet, we will practice relating the impulse on a body to the change of momentum of the body.

**Q1: **

A constant force acted on a body of mass 6 kg. As a result, its speed changed from 37 km/h to 49 km/h. Calculate the magnitude of the impulse of this force on this body.

**Q2: **

A smooth sphere of mass 1,412 g was moving horizontally in a straight line at 13.5 m/s when it hit a smooth vertical wall and rebounded at 9 m/s. Determine the magnitude of the impulse exerted on the sphere.

**Q3: **

The given figure shows a forceβtime graph for a force acting in a constant direction on a body moving along a smooth horizontal plane. Using the information provided, calculate the magnitude of the forceβs impulse.

**Q4: **

A constant force acted on a body of mass changing its speed from 9 m/s to 54 km/h. Given that the impulse of the force was 5.82 Nβ s, determine the value of .

**Q5: **

The forces , , and acted on a body for 3 seconds. If their combined impulse on the body was , find the values of and .

- A,
- B,
- C,
- D,

**Q6: **

Three forces, , , and , where , , and are three mutually perpendicular unit vectors, acted on a body for 3 s. Find the magnitude of their combined impulse on the body.

- A27 Nβ s
- B Nβ s
- C Nβ s
- D9 Nβ s

**Q7: **

A body of mass 5 kg fell vertically from rest. It reached the waterβs surface after 2.2 s. Then, as it moved through the water, it descended vertically with a constant speed such that it covered 3.9 m in 1.5 s. Find the magnitude of the change in its momentum as a result of its impact with the water.

**Q8: **

The given figure shows a forceβtime graph. At time s, where , the force is given by . Find the impulse over the first four seconds.

- A4 Nβ s
- B8 Nβ s
- C Nβ s
- D Nβ s

**Q9: **

A ball of mass 400 g moves perpendicularly toward a vertical wall at a constant speed of 16 m/s. Given that the wall exerts an impulse of 11 Nβ s on the ball during the impact, find the rebound speed of the ball.

- A5.75 m/s
- B27.5 m/s
- C11.5 m/s
- D19.5 m/s

**Q10: **

A sphere of mass 83 g fell vertically from a height of
8.1 m onto a section of horizontal ground. It
rebounded and reached a height of 3.6 m. Given that the duration of the
impact was 0.42 s, and the acceleration due to gravity
is 9.8 m/s^{2},
find the average impact force to the nearest two decimal places.