1. A projectile is shot from the edge of a cliff 140 m above ground level with an initial speed of 100 m/s at an angle of 37.0 with the horizontal, as shown in the figure. Use 3 significant figures. a.) Determine the time taken by the projectile to hit point P at ground level. b.) Determine the range X of the projectile as measured from the base of the cliff. Ki Xf At the instant just before the projectile hits point P, find yi Vf c.) the horizontal (Vfx) and the vertical (Vfy) components of its velocity Vix Vfx d.) If the speed the tennis ball is hit is doubled, will the time the projectile is in the air increase, stay the same or decrease. Check Viy Viv the appropriate box. e.) If the speed the tennis ball is hit is doubled, will the distance ax the projectile travels (X) increase, stay the same or decrease. ay Check the appropriate box. Do = 100 m/s 370 a. b. h= 140 m C. d. increase same decrease levitt laxt e. increase same decrease2. At serve, a tennis player aims to hit the ball horizontally. a.) What minimum speed is required for the ball to clear the 0.90-m-high net about 15.0 m from the server if the ball is "launched" from a height of 2.50 m? [Hint: put final position at net (f)]. b.) Where will the ball land if it just clears the net (and will it be "good" in the sense that it lands within 7.0m of the net)? [ Hint: put final position on the court (f2)] c.) How long will it be in the air? d.) If the speed the tennis ball is hit is doubled, will the time the ball is in the air increase, stay the same or decrease. Check the appropriate box. e.) If the tennis ball was hit on the moon instead of earth (gmoon = 1/6 gearth, will the time the ball is in the air increase, stay the same or decrease. Check the appropriate box. 2.50 m 15.0 m - -7.0 m Ki Xf Xf2 yi yf yf2 Vix Vix Vf2,x Viy Vfy Vf2,y ax av a. b. Good? Yes No C. d. increase same decrease e. increase same decrease3. A footba kicked at an angle of 60.0 with respect to the horizontal. The football is kicked at a speed of 25.0 m/s. Neglecting air resistance, find the following: a.) Include a coordinate system and label initial and final values. b.) Complete the table with known information. c.) The time the football is in the air. Xi Xf d.) How far does the football go? yi yf e.) Graph Vx vs. time. Label the values of the horizontal and vertical axes. Vix Vfy f.) Graph Vy vs. time. Label the values of the horizontal and vertical axes. Viy VA g.) Graph ax and ay vs. time. Label the values of the horizontal and vertical axes. ax 25.0 m/s a .0'09 = 0 e, f, g.) C. Horizontal d. Velocity (m/s) Time (s) Vertical Velocity (m/s) Time (s) X ax, ay (m/s2) time (s)4. A ball of mass 0.5 kilogram, initially at rest, is kicked directly toward a fence from a point 32 meters away, as shown. The velocity of the ball as it leaves the kicker's foot is 20 meters per second at an angle of 37 above the horizontal. The top of the fence is 2.5 meters high. The ball hits nothing while in flight and air resistance is negligible. a. Determine the time it takes for the ball to reach the plane of the fence. Hint: put the final position when the ball is at the fence. b. Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how far above the top of the fence will it pass? Hint: find ys as the ball gets to the fence. If ys is less than 2.5 m, it hits the fence; if ys is greater than 2.5 m, it clears the fence. c. On the axes below, sketch the horizontal and vertical components of the velocity of the ball as functions of time until the ball reaches the plane of the fence. 20 * - Xi Af 15 Vi yf Horizontal' Vi Vf Component of Velocity 01## + Time (8 ) (m/s) 0.5 1.0 3. 0 Vi 3.5 -5 ax av -10] -15 20 t-. a. b. Hit the fence: Vertical Yes No Component of Velocity OF Time (s) (m/s) 0.5 1.0 1.5 20 2.5 3.0 3.5 4.0 b. How far above or -5 below the top of the fence? -10 -15 -20 7_