Near the middle of the term, Avi and Cameron are taking their laboratory exam. The instructor has given them a spring-loaded ball launcher. The instructor explains how the launcher works: The ball compresses a spring, and when the trigger is pressed, the ball is released. The spring is always compressed by the same amount, and so the muzzle speed of the ball is essentially the same each time the ball is released. The angle of the launcher may be adjusted from 0° to 90°, where 0° is horizontal and 90° is straight up. The instructor has fixed a canister on their laboratory bench and tells them they will be given one chance to launch the ball such that it lands in the canister. She has marked a spot on the floor upon which the launcher must be placed. Finally, she tells them they may have one chance to launch the ball before the "real" test. Read Avi and Cameron's discussion, and think about who you agree with before you answer the questions. Avi: It seems to me the real trick is finding the right angle. We have no choice about where to put the launcher or the height of the can. Cameron: Yeah, I see that, but it almost seems too easy. We just measure the height of the can and the distance to the can. Then we get the angle using the inverse-tangent. Avi: We'll need those distances, but the angle is going to be hard to find. The ball won't be traveling in a straight line. Plus we'll need to find the muzzle speed of the launcher. Cameron: We won't need the speed because we don't need to know how long it takes to make the shot; we just need to aim it. The aim is the angle we get from taking the inverse-tangent of those measurements. Avi: I know we don't care about the time, but we still need the speed. The angle will come from the range equation R = (vg) sin(20) for projectile motion. Remember, the ball moves in a parabolic arc. Cameron: No. That can't be right. We can only use the range equation when the ball lands at the same height. You remember, no change in y.

Near the middle of the term, Avi and Cameron are taking their laboratory exam. The instructor has given them a spring-loaded ball launcher. The instructor explains how the launcher works: The ball compresses a spring, and when the trigger is pressed, the ball is released. The spring is always compressed by the same amount, and so the muzzle speed of the ball is essentially the same each time the ball is released. The angle of the launcher may be adjusted from 0° to 90°, where 0° is horizontal and 90° is straight up. The instructor has fixed a canister on their laboratory bench and tells them they will be given one chance to launch the ball such that it lands in the canister. She has marked a spot on the floor upon which the launcher must be placed. Finally, she tells them they may have one chance to launch the ball before the "real" test. Read Avi and Cameron's discussion, and think about who you agree with before you answer the questions. Avi: It seems to me the real trick is finding the right angle. We have no choice about where to put the launcher or the height of the can. Cameron: Yeah, I see that, but it almost seems too easy. We just measure the height of the can and the distance to the can. Then we get the angle using the inverse-tangent. Avi: We'll need those distances, but the angle is going to be hard to find. The ball won't be traveling in a straight line. Plus we'll need to find the muzzle speed of the launcher. Cameron: We won't need the speed because we don't need to know how long it takes to make the shot; we just need to aim it. The aim is the angle we get from taking the inverse-tangent of those measurements. Avi: I know we don't care about the time, but we still need the speed. The angle will come from the range equation R = (vg) sin(20) for projectile motion. Remember, the ball moves in a parabolic arc. Cameron: No. That can't be right. We can only use the range equation when the ball lands at the same height. You remember, no change in y.