Chapter 4: Kinematics in Two Dimensions

You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30° above horizontal, the ball hits the bull’s-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit the bull’s-eye in its new position? (Mathematically there are two solutions to this problem; the physically reasonable answer is the smaller of the two.)

A 35 g steel ball is held by a ceiling-mounted electromagnet 3.5 m above the floor. A compressed-air cannon sits on the floor, 4.0 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls collide 1.0 m above the floor. What was the launch speed of the plastic ball?

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 60 m away, making a 3.0° angle with the ground. How fast was the arrow shot?

You’re 6.0 m from one wall of the house seen in FIGURE P4.55. You want to toss a ball to your friend who is 6.0 m from the opposite wall. The throw and catch each occur 1.0 m above the ground.

a. What minimum speed will allow the ball to clear the roof?

b. At what angle should you toss the ball?

Sand moves without slipping at 6.0 m/s down a conveyer that is tilted at 15°. The sand enters a pipe 3.0 m below the end of the conveyer belt, as shown in FIGURE P4.56. What is the horizontal distance d between the conveyer belt and the pipe?

A stunt man drives a car at a speed of 20 m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20°.

a. How far from the base of the cliff does the car land?

b. What is the car’s impact speed?

A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 30° above the horizontal. Top-rated javelin throwers do throw at about a 30° angle, not the 45° you might have expected, because the biomechanics of the arm allow them to throw the javelin much faster at 30° than they would be able to at 45°. In this throw, the javelin hits the ground 62 m away. What was the acceleration of the javelin during the throw? Assume that it has a constant acceleration.

A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the “law of reflection,” which says that the ball leaves the surface at the same angle it approached the surface. The ball’s next bounce is 3.0 m to the right of its first bounce. What is the ball’s rebound speed on its first bounce?

6. A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of $v_x$and $v_y$, the x - and y-components of the puck's velocity. The puck starts at the origin.

a. In which direction is the puck moving at ? Give your answer as an angle from the x-axis.

b. How far from the origin is the puck at ?

A cart that is rolling at constant velocity on a level table fires a ball straight up.

a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or directly in the tube? Explain.

b. Will your answer change if the cart is accelerating in the forward direction? If so, how?