Engineering Mathematics (MTH1150)
Final Review Questions
1. A person throws a ball (m = 0.20 kg) with a force of 25 N. The displacement of the
ball is 1.6 m as the force was being applied. What was the velocity of ball when it
was released?
2. Two people are lifting a heavy box (625 N). One person is applying a force of 400 N
at an angle of 40 degrees from the horizontal. The other person is applying a force of
320 N. At what angle should the second force be applied so the box will accelerate
straight up? How fast will the object be moving after 1 second?
3. Four College students simultaneously grasp the last piece of pizza (m = 150 g). One
exerts a force of 15 N at an angle of 20 degrees; the second exerts a force of 22 N at
an angle of 95 degrees; the third student exerts a force of 8 N at an angle of 160
degrees; and the fourth exerts a force of 16 N at an angle of 210 degrees. At what
acceleration and angle will the pizza move?
4. A motorbike with a mass of 375 kg is travelling at 120 km/h and makes an emergency
stop in 35 m. What is the coefficient of kinetic friction (assuming skidding) between
the tires and the road?
5. You want to design a steel slide to move steel parts from the first story to the second
story of a building (assume 4 meters between stories). The slide should be designed
so the parts will begin to slide on their own (without an additional force). What is the
velocity of the part when it reaches the second floor?
6. What is the maximum speed should you post on a banked (8 degrees) curve on a
highway? The curve has a radius of 55 m. Considering poor driving conditions, we
will use a coefficient of static friction = 0.30 (rubber on wet concrete).
7. Design a rope that will lift a 2750 kg object a displacement of 15 meters straight up in
10 seconds (assuming a constant acceleration). How much power is required?
8. Given a rope with a breaking strength of 10000 N, what is
the maximum mass that can be lifted 5.0 meters higher in
15 seconds (shown in the scenario)?
9. A 13.13 kg object is raised vertically 15.6 by a block & tackle from a standstill. The
velocity is 3.6 m/s at this point. How much work is done?
10. An 80-kg object is held stationary at 100 m from the ground. It is then dropped. What
is the velocity at 30 m from the ground?
11. A 25-kg box is placed on an inclined plane at
an angle of 35° from the horizontal. The
friction losses are measured at 23 J, and it
reaches a velocity of 5.8 m/s at the end of the
slide. What is the length of the slide?
12. A steel box with the dimensions of 3.0500m x 1.8900m x 0.2500m at 25°C is put in
the freezer at a temperature of -28°C. What is the change in volume of the box?
13. A 3.12 kg steel bar at 554°C is placed in 0.85 kg of water at 36°C. What is the
equilibrium temperature?
14. Compute 𝑓 ′ (𝑥) for the following equations using the definition of a derivative:
a) 𝑦 = 3𝑥 2 + 3𝑥
1
b) 𝑦 = 𝑥 2
c) 𝑦 = 𝐴𝑥 2 + 𝐵𝑥 + 𝐶
15. Find the equation of a tangent line to the functions from the previous question
(excluding question c) at x = 3.
𝑑𝑦
16. Find 𝑑𝑥 for the following equations:
a) 𝑦 = −5𝑥 3 + 4𝑥 − 10
b) 𝑦 = √𝑥 − 1(3𝑥 2 + cos(𝑥))
𝑥 √𝑥
c) 𝑦 = 𝑥−1
d) 𝑦 = (10𝑥 − 5)5
e) 𝑦 =
f) 𝑦 =
g) 𝑦 =
h) 𝑦 =
𝜋
cos(𝜋𝑥)
3𝑥 3 +4
9
cos(𝑥)
𝜋
2𝑥 2 −3
3−𝑥 2
17. At what points does the line tangent to 𝑦 = 𝑥 2 at 𝑥 = 2 intersect the circle
𝑥 2 + 𝑦 2 = 9?
18. An objects position is defined by the function 𝑥(𝑡) = 3𝑥 3 − 9𝑥 2 − 5 𝑚. Answer the
following questions:
a)
b)
c)
d)
What is the objects position at t = 1s?
What is the objects velocity at t = 1s?
What is the objects acceleration at t = 1s?
Was the object moving forward or backwards at t = 1s?