**BMAT Prep Question Analysis - Q117 & Q209**

**Q117 A 2,000 kg car travelling at 30 m/s crashes into a 5,000 kg truck that is originally at rest. What is the speed of the truck after the collision, if the car comes to rest at the point of impact? (Ignore friction)**

a. 2 m/s

b. 4 m/s

c. 8 m/s

d. 10 m/s

e. 12 m/s

**Q209 The average height of 3 members of a five-a-side football team is 175cm. What does the average height in centimetres of the other 2 players have to be if the average height of the entire team equals 178cm?**

a. 178cm

b. 181cm

c. 182.5cm

d. 183.5cm

e. 184cm

**Answer and Explanation**

**Q117** **Answer**: e. 12 m/s

**Explanation**:

The sum of the momentums before the collision is equal to the sum of the momentum after the collision (since friction is ignored) and we need to use the conservation of momentum equation to determine the speed of the truck after the impact: M = mass and U = velocity.

Mcar U(car)initial + Mtruck U(truck)initial = Mcar U(car)final + Mtruck U(truck)final

(2000 x 30) + (5000 x 0) = (2000 × 0) + (5000 x U(truck)final)

U(truck)final = 60,000/5,000 = 12 m/s

**Q209 Answer: **c. 182.5cm

**Explanation: **

The sum of the heights of the 3 members is 3 x 175 = 525cm.

If the average across the whole team of 5 members is 178cm then the sum of their heights is 5 x 178 = 890.

So, the sum of the heights of the remaining 2 players is: 890-525=365cm and, consequently, their average height is 365/2 = 182.5cm.

Drafted by Quincy (BMAT Prep)