The van is traveling at $20 \mathrm{~km} / \mathrm{h}$ when the coupling of the trailer at $A$ fails. If the trailer has a mass of $250 \mathrm{~kg}$ and coasts $45 \mathrm{~m}$ before coming to rest, determine the constant horizontal force $F$ created by rolling friction which causes the trailer to stop.

Calculate the constant speed of the cars on the amusement-park ride if it is observed that the cables are directed at $30^{\circ}$ from the vertical. Each car, including its passengers, has a mass of $550 \mathrm{~kg}$. Also, what are the components of force in the $n, t$, and $z$ directions which a 60 -kg passenger exerts on the car during the motion?

The two blocks A and B each have a mass of 400 g. The blocks are fixed to the horizontal rods, and their initial velocity along the circular path is 2 m/s. If a couple moment of M=(0.6) N.m is applied about C D of the frame, determine the speed of the blocks when t=3 s. The mass of the frame is negligible, and it is free to rotate about CD. Neglect the size of the blocks.

The 6-lb particle is subjected to the action of its weight and forces $\mathbf{F}_1=\{2 \mathbf{i}+6 \mathbf{j}-2+\mathbf{k}\} \mathrm{lb}, \quad \mathbf{F}_2=$ $\left\{t^2 \mathbf{i}-4 t \mathbf{j}-1 \mathbf{k}\right\} \mathrm{lb}$, and $\mathbf{F}_3=\{-2 \boldsymbol{i}\} \mathrm{lb}$, where $t$ is in seconds. Determine the distance the ball is from the origin 2 s after being released from rest.

A 300-g ball is kicked with a velocity of $v_A = 25$ m/s at point A as shown. If the coefficient of restitution between the ball and the field is e = 0.4, determine the magnitude and direction u of the velocity of the rebounding ball at B.

The girl throws the ball with a horizontal velocity of $v_1=8 \mathrm{ft} / \mathrm{s}$. If the coefficient of restitution between the ball and the ground is e=0.8, determine

(a) the velocity of the ball just after it rebounds from the ground and

(b) the maximum height to which the ball rises after the first bounce.

The motorcycle has a mass of $0.5 \mathrm{Mg}$ and a negligible size. It passes point $A$ traveling with a speed of $15 \mathrm{~m} / \mathrm{s}$, which is increasing at a constant rate of $1.5 \mathrm{~m} / \mathrm{s}^2$. The radius of curvature of road at point $A$ is $\rho_{A} = 200 \text{ m}$. Determine the resultant frictional forcce exerted by the road on the tires at this instant.

In the following budget constraint–indifference curve graph, Nikki has $200 to spend on tops and pants.

Is Nikki making the optimum choice if she buys 4 tops and 2 pants? Explain how you know this.

The three balls each weigh 0.5 lb and have a coefficient of restitution of e = 0.85. If ball A is released from rest and strikes ball B and then ball B strikes ball C, determine the velocity of each ball after the second collision has occurred. The balls slide without friction.

At the instant, the $3000-\mathrm{lb}$ car is traveling with a speed of $75 \mathrm{ft} / \mathrm{s}$, which is increasing at a rate of $6 \mathrm{ft} / \mathrm{s}^2$. Determine the magnitude of the resultant frictional force the road exerts on the tires of the car. Neglect the size of the car. The radius of road curvature is $600\mathrm{~ft}$.

A communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the rotation of the earth, which is approximately 24 hours. Determine the satellite’s altitude h above the earth’s surface and its orbital speed.

A car travels along a road, which for a short distance is defined by $r=(200 / \theta) \mathrm{ft}$, where $\theta$ is in radians. If it maintains a constant speed of $v=35 \mathrm{ft} / \mathrm{s}$, determine the radial and transverse components of its velocity when $\theta=\pi / 3 \mathrm{rad}$.

A car travels along a road, which for a short distance is defined by $r=(200 / \theta) \mathrm{ft}$, where $\theta$ is in radians. If it maintains a constant speed of $v=35 \mathrm{ft} / \mathrm{s}$, determine the radial and transverse components of its velocity when $\theta=\pi / 3 \mathrm{rad}$

The position of a particle is described by $r=\left(t^3+4 t-4\right) \mathrm{m}$ and $\theta=\left(t^{3 / 2}\right) \mathrm{rad}$, where $t$ is in seconds. Determine the magnitudes of the particle's velocity and acceleration at the instant $t=2 \mathrm{~s}$.