A rock is thrown from the top of a $20-\mathrm{m}$ building at an angle of $53^{\circ}$ above the horizontal. If the horizontal range of the throw is equal to the height of the building, with what speed was the rock thrown? What is the velocity of the rock just before it strikes the ground?

Suppose your effort work, and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is A. Zero B. Less than the force of the rope on the car. C. Equal to the force of the rope on the car. D. Greater than the force of the rope on the car.

A football is kicked straight up into the air; it hits the ground 5.2 s later.

With what speed did it leave the kicker's foot?

A football is kicked straight up into the air; it hits the ground 5.2 s later.

What was the greatest height reached by the ball? Assume it is kicked from ground level.

Excellent human jumpers can leap straight up to a height of 110 cm off the ground. To reach this height, with what speed would a person need to leave the ground?

A toy cannon is placed on a ramp that has a slope of angle $\phi$. (a) If the cannonball is projected up the hill at an angle of $\theta_0$ above the horizontal (Figure 3-39) and has a muzzle speed of $v_0$, show that the range $R$ of the cannonball (as measured along the ramp) is given by $R=\frac{2 v_0^2 \cos ^2 \theta_0\left(\tan \theta_0-\tan \phi\right)}{g \cos \phi}$. Ignore any effects due to air resistance.

A stone is thrown horizontally from the top of an incline that makes an angle $\theta$ with the horizontal. If the stone's initial speed is $v_0$, how far down the incline will it land?

A projectile, fired with unknown initial velocity, lands $20 \mathrm{~s}$ later on the side of a hill, $3000 \mathrm{~m}$ away horizontally and $450 \mathrm{~m}$ vertically above its starting point. (a) What is the vertical component of its initial velocity? (b) What is the horizontal component of its initial velocity?

A golfer drives the ball from the tee down the fairway in a high arcing shot. When the ball is at the highest point of its flight, $(a)$ its velocity and acceleration are both zero, $(b)$ its velocity is zero but its acceleration is nonzero, (c) its velocity is nonzero but its acceleration is zero, $(d)$ its velocity and acceleration are both nonzero, $(e)$ insufficient information is given to answer correctly.

Can the magnitude of the displacement of a particle be less than the distance traveled by the particle along its path? Can its magnitude be more than the distance traveled? Explain.

A speeding car is traveling at a constant velocity of $V_1=30\:\dfrac{\text{m}}{\text{s}}$ when is passes by the stationary police car. If the policeman has a delayed reaction of $t=1\text{ s}$, what is the required magnitude of the acceleration of the police car in order to catch the speeding car after the $\Delta s=300\text{ m}$?

Three vectors are shown in Fig. 3-41. Their magnitudes are given in arbitrary units. Find the sum of the three vectors. Give the resultant in terms of components.

Estimate the number of atoms in 1 cm$^3$ of a solid. (Note that the diameter of an atom is about 10$^{-10}$ m.)

Suppose your hair grows at the rate of 1/32 inch per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, your answer suggests how rapidly atoms are assembled in this protein synthesis.