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Name _____________________________
Projectile Motion Packet
Period ______
Date ____________________
1. The height of an object, h(t), is determined by the formula h(t) = –16t 2 + 256t, where t is time, in seconds.
Will the object reach a maximum or a minimum? Justify your answer.
2. A rock falls from the top of a cliff to the ocean 100 feet below. The distance, S, the rock is from the ocean
as it falls is represented by the equation S(t) = –16t 2 + 100, where t represents time, in seconds. How long
does it take for the rock to hit the water?
A) 2.0 s
B) 2.5 s
C) 5.0 s
D) 6.3 s
3. The distance X of a runner from his starting position at time t is given by the equation What is the runner's maximum distance from his starting point between t = 0 and t = 10?
A) 10
B) 25
C) 50
.
D) 100
4. A frog leaps into the air at an initial velocity of 16 inches per second. The height of the frog t seconds after
it leaps is given by the formula f(t) = 16t – 4t 2. How many seconds after the frog leaps into the air will it
return to the ground?
5. The equation of a ball that is thrown up into the air is y = –(x – 2.25)2 + 6, 0 x 6, where x is measured in
seconds and y is measured in feet. What is the maximum height reached by the ball, in feet?
6. A rocket is fired from a cannon that is on the ground. The function below represents the distance, in
feet, that the ball is from the ground at any time . At what time, to the nearest hundredth of a second, is the
rocket at its maximum height?
A)
B)
C)
D)
7. An acorn falls from the branch of a tree to the ground 64 feet below. The distance, S, the acorn is from the
ground as it falls is represented by the equation S(t) = –16t 2 + 64, where t represents time, in seconds. Approximately how long does it take for the acorn to reach the ground?
A) 2 s
B) 4 s
C) 8 s
D) 16 s
8. The height, h, in feet, a ball will reach when thrown in the air is a function of time, t, in seconds, given by
the equation h(t) = –16t2 + 30t + 6. Find, to the nearest tenth, the maximum height, in feet, the ball will
reach.
9. A ball is thrown straight up at an initial velocity of 54 feet per second. The height of the ball t seconds after
it is thrown is given by the formula h(t) = 54t – 12t 2. How many seconds after the ball is thrown will it
return to the ground?
A) 9.2
B) 6
C) 4.5
D) 4
10. An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the
equation y = –2x 2 + 12x, where y is the height of the arch.
a Graph the parabola from x = 0 to x = 6 on the grid below.
b Determine the maximum height, y, of the arch.