Quadratic Word Problem Worksheet
1. If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per
second, then its height h after t seconds is given by the equation h(t )  16t 2  128t .
a) How long will it take for the rocket to return to the ground?
b) After how many seconds with the rocket be 112 feet above the ground?
c) How long will it take the rocket to hit is maximum height?
2. A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 feet per second.
a) Substitute the values into the formula h(t )  16t 2  vt  h0 ; h0 is initial height.
b) Use the quadratic formula to find out how long the rocket will take to hit the ground after it is
launched. Round to the nearest tenth of a second.
c) What is the maximum height the rocket will reach?
3. A diver is standing on a platform 24 feet above the pool. He jumps from the platform with an initial
velocity of 8 feet per second. Use the formula h(t )  16t 2  vt  h0 .
a) How long will it take the diver to hit the water?
b) When will the diver be at his maximum height?
4. You and a friend are hiking in the mountains. You want to climb to the ledge that is 20 feet above
you. The height of the grappling hook you throw is given by the function h(t )  16t 2  32t  5 .
a) What is the maximum height of the grappling hook?
b) Can you throw it high enough to reach the ledge?
5. During World War I, mortars were fired from trenches 3 feet down. The mortars had a velocity of
150 ft/s. Determine how long it will take for the mortar shell to strike its target.
6. A rectangular field will be fenced on all four sides. There will also be a line of fence across the field,
parallel to the shorter side. If 900 m of fencing are available, what dimensions of the field will produce
the maximum area? What is the maximum area?
7. A water balloon is catapulted into the air so that its height h, in meters,
after t seconds is h(t )  4.9t 2  27t  2.4 .
a) How high is the balloon after 1 second?
b) For how long is the balloon more than 30 m high?
c) What is the maximum height of the balloon?
d) When will the balloon burst as it hits the ground?
8. Among all pairs of numbers whose difference is 24, find a pair whose product is as small as possible.
What is the minimum product?
9. You have 600 feet of fence to enclose a rectangular plot of land that boarders a river. If you do not
fence the side along the river, find the length and width of the plot that will maximize the area. What is
the largest area that you can enclose?
10. A rectangular plot is to be fenced off and divided in two by placing another fence parallel to one side
of the rectangle. 400 feet if fence is used in total to build this enclosure. Find the dimensions of the
rectangular plot that would maximize the area.
Find the maximum area.