In a baseball practice, Jacob threw the ball such that , its height above the ground in feet seconds after he released it, could be modeled by the quadratic equation
Write an equation that could be solved to find the times at which the ball was at a height of 33 feet above the ground.
For how long was the ball 33 feet above the ground?
A missile is launched vertically upward at a speed of 362.6 m/s.
Its height above the point from which it was launched can be found using where m is the height above the launch point, m/s is its speed when it was launched, and s is the time after it was launched. Find the times at which the missile is at a height of 6 629.7 m above the launch point.
The height of a missile above its launch point can be found using where m is the height above the launch point, m/s is the vertical launch speed, and s is the time after launch. A missile is launched vertically upwards with a speed of 49 m/s. At what times will it be 44.1 m above its launch point?
A diver jumped from a board 15 meters above the surface of the water. The height of the dive can be found using the equation , where after seconds, the diver is meters above the water. Determine the time it took for the diver to reach the water, giving your answer to 2 decimal places.
After seconds, the height, , of a diver above the surface of the pool is given by the equation . How long does it take for the diver to reach the water?
A sprinkler is used to water a garden. The height , in meters, of the jet of water a horizontal distance meters from the sprinkler can be found using the quadratic equation
Write an equation that will give the distance, in meters, between the sprinkler and the point where the jet hits the ground.
How far from the sprinkler does the jet hit the ground?
The arch of a curved iron gate with side length 5 m can be represented by the function . Find the value of .
The arch of a curved iron gate with side length 3 m can be represented by the function . Find the maximum height and width of the gate.
A projectile is launched vertically upward at a speed of 120 ft/s from a 5-foot-high pad. Its height , seconds after it is launched, is modeled by the formula . Find, to the nearest hundredth of a second, the times at which the projectile is at a height of 100 ft.
A toy rocket’s height, feet above the ground, is described by the equation , where feet is the horizontal distance traveled. What is the distance between the point it takes off and the point it lands?
At an athletics competition, the flight path of the discus thrown by one of the competitors can be described by the equation , where is the height of the discus above the ground in meters when it has traveled a horizontal distance of meters. How far does the discus travel horizontally before it hits the ground for the first time?
A garden is watered using a hose. The path of the water can be described by the equation , where is the height of the water above the ground in meters when it is a horizontal distance of meters from the hose. What is the maximum value of to the nearest cm?
A child threw a ball vertically upwards with a speed m/s. The ball’s height above the ground seconds after it was thrown was 8 meters. The values of and satisfy the equation .
If the ball reached 8 m after a quarter of a second, at what speed was it thrown?
If the ball’s initial speed was 16 m/s, for how long was it higher than 8 m?