Q: A projectile is launched at speed $$v_0$$ and angle $$\theta. $$What is the formula for the range $$R ($$horizontal distance traveled)?

$$R = \frac{v_0$^2 \sin(2\theta)}{g}$$

Question 1

A car travels 40 km at 30 km/h and then another 40 km at 60 km/h in the same direction. What is the average velocity for the entire trip?

Accepted Answer

$$40\ \mathrm{km/h}$$

Question 2

A ball is thrown horizontally from a 45 m high bridge and lands 12 m away from the base. What is the speed of the ball in the horizontal direction?

Accepted Answer

$$4.0\ \mathrm{m/s}$$

Question 3

A 10 kg object is pushed up a frictionless ramp at $$	heta = 30^\circ at $$constant speed by a horizontal force $$\vec{F}. $$What is the magnitude of $$\vec{F}$$?

Accepted Answer

$$56.6\ \mathrm{N}$$

Question 4

A rabbit's position is given by $$x(t) = -0.31t^2$ + 7.2t + 28$$ and $$y(t) = 0.22t^2$ - 9.1t + 30. $$What is the magnitude of the velocity at $$t = 15\ \mathrm{s}$$?

Accepted Answer

$$3.3\ \mathrm{m/s}$$

Question 5

A 3.5 kg block is pushed along a horizontal floor by a force of 15 N at $$40^\circ$$ above the horizontal. The coefficient of kinetic friction is $$0.25. $$What is the magnitude of the frictional force?

Accepted Answer

$$11.0\ \mathrm{N}$$

Question 6

A 2.0 kg sloth hangs 5.0 m above the ground. What is its gravitational potential energy relative to the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$98.0\ \mathrm{J}$$

Question 7

A block of mass $$m = 2.0\ \mathrm{kg} is $$dropped from a height $$h = 0.40\ \mathrm{m}$$ onto a spring with $$k = 1960\ \mathrm{N/m}. $$What is the maximum compression $$y of $$the spring?

Accepted Answer

$$0.10\ \mathrm{m}$$

Question 8

A puck of mass $$m = 1.50\ \mathrm{kg}$$ slides in a circle of radius $$r = 0.20\ \mathrm{m} on a $$frictionless table, attached to a hanging mass $$M = 2.50\ \mathrm{kg}. $$What speed keeps the cylinder at rest?

Accepted Answer

$$1.81\ \mathrm{m/s}$$

Question 9

A 100 kg ball moving at $$10\ \mathrm{m/s}$$ compresses a spring by $$0.5\ \mathrm{m}$$ and comes to rest. What is the spring constant $$k$$?

Accepted Answer

$$40,000\ \mathrm{N/m}$$

Question 10

A car slows down uniformly from $$28\ \mathrm{m/s} to $$rest in $$8\ \mathrm{s}. $$What is the distance traveled?

Accepted Answer

$$112\ \mathrm{m}$$

Question 11

A force of $$5\ \mathrm{N}$$ acts on a box for $$3\ \mathrm{m} to $$the left. What is the work done by the force if it acts at $$0^\circ to $$the displacement?

Accepted Answer

$$15\ \mathrm{J}$$

Question 12

A 72 kg astronaut is lifted 15 m vertically by a helicopter with an acceleration of $$g/10. $$What is the net work done on the astronaut?

Accepted Answer

$$1.0\ \mathrm{kJ}$$

Question 13

A block is pulled by a force $$F at an $$angle $$	heta$$ above the horizontal. The normal force $$F_N is $$given by:

Accepted Answer

$$F_N = mg - F\sin	heta$$

Question 14

A race car of mass $$600\ \mathrm{kg}$$ travels through a flat turn of radius $$100\ \mathrm{m} at$$ $$29\ \mathrm{m/s}. If$$ $$\mu_s = 0.75$$, what is the required downforce $$F_D to $$prevent sliding?

Accepted Answer

$$848\ \mathrm{N}$$

Question 15

A spring stores $$25\ \mathrm{J} of $$elastic potential energy when compressed by $$7.5\ \mathrm{cm}. $$What is the spring constant $$k$$?

Accepted Answer

$$8,333\ \mathrm{N/m}$$

Question 16

A projectile is launched at speed $$v_0$$ and angle $$	heta. $$What is the formula for the range $$R ($$horizontal distance traveled)?

Accepted Answer

$$R = \frac{v_0$^2 \sin(2	heta)}{g}$$

Question 17

Which of the following is true about conservative forces?

Accepted Answer

The work done depends only on the initial and final positions.

Question 18

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 19

A force acts perpendicular to the displacement of an object. What is the work done by this force?

Accepted Answer

$$W = 0$$

Physics with Calculus: Kinematics, Dynamics, and Work-Energy Principles

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