Quadratic Word Problems
Directions: Answer each of the following questions algebraically. You may sketch the graph of the parabola to help you visualize the flight of the ball.
1. A water balloon is tossed into the air with an upward velocity of 25ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = -16t2 + 25t + 3. a) After how many seconds will the balloon hit the ground? b) What will the height be at t = 1 second?
2. A football is passed through the air and caught at ground level for a touchdown. The height h of the ball in feet is given by h = -d2 + 12d + 6, where d is the distance in feet the ball travels horizontally. How far from the player passing the ball will the ball be caught?
3. A basketball is passed through the air. The height h of the ball in feet after the distance d in feet the ball travels horizontally is given by h = -d2 + 10d + 5. How far horizontally from the player passing the ball will the ball land on the ground?
4. A golf ball is driven in the air toward the hole from an elevated tee with an upward velocity of 160 ft/s. Its height h in feet after t seconds is gen by the function h = -16t2 + 160t + 18. How long will it take for the golf ball to reach its maximum height? What is the golf ball’s maximum height?
5. A baseball player hit a ball with an upward velocity of 46 ft/s. Its height h in feet after t seconds is given by the function h = -16t2 + 46t + 6. What is the maximum height the ball reaches? How long will it take the baseball to reach the maximum height? How long does it take for the ball to hit the ground?
6. A golf ball is chipped into the air from a small hill with an upward velocity of 50 ft/s. Its height h in feet after t seconds is given by the function h = -16t2 + 50t + 10. What is the maximum height? How long does it take for the ball to hit the ground?
7. A punter kicked the football into the air with an upward velocity of 62 ft/x. Its height h
1. A water balloon is tossed into the air with an upward velocity of 25ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = -16t2 + 25t + 3. a) After how many seconds will the balloon hit the ground? b) What will the height be at t = 1 second?
2. A football is passed through the air and caught at ground level for a touchdown. The height h of the ball in feet is given by h = -d2 + 12d + 6, where d is the distance in feet the ball travels horizontally. How far from the player passing the ball will the ball be caught?
3. A basketball is passed through the air. The height h of the ball in feet after the distance d in feet the ball travels horizontally is given by h = -d2 + 10d + 5. How far horizontally from the player passing the ball will the ball land on the ground?
4. A golf ball is driven in the air toward the hole from an elevated tee with an upward velocity of 160 ft/s. Its height h in feet after t seconds is gen by the function h = -16t2 + 160t + 18. How long will it take for the golf ball to reach its maximum height? What is the golf ball’s maximum height?
5. A baseball player hit a ball with an upward velocity of 46 ft/s. Its height h in feet after t seconds is given by the function h = -16t2 + 46t + 6. What is the maximum height the ball reaches? How long will it take the baseball to reach the maximum height? How long does it take for the ball to hit the ground?
6. A golf ball is chipped into the air from a small hill with an upward velocity of 50 ft/s. Its height h in feet after t seconds is given by the function h = -16t2 + 50t + 10. What is the maximum height? How long does it take for the ball to hit the ground?
7. A punter kicked the football into the air with an upward velocity of 62 ft/x. Its height h