Alan is standing on a hill 80 feet high. He throws a baseball upward with
an initial velocity of 64 feet per second. The height of the ball
h(t) in terms of the time t since the ball was thrown is
h(t) = -16t2 + 64t + 80.
a) Find the time that the ball reaches its max height
b) Find the max height
c) Find the time when the ball hits the ground
1
A projectile is launched at a speed of 40 meters per second from a 89­meter tall platform. The equation for the object’s height S at time t seconds after launch is S (t) = ­4.9t2 + 40t + 89, where S is in meters. How long will it take for the object to reach its maximum height? When will it reach a height of 50m above the ground? Round all of your answers to the nearest hundredth.
2
Jessica, who has a bionic arm, is crossing a bridge over a small gorge and decides to toss a coin into the stream below for luck. The distance of the coin above the water can be modeled by the function y = ­16x2 + 96x + 112, where x measures the time in seconds and y measures the height, in feet, above the water.
a) Find the greatest height the coin reaches before it drops into the water below.
b) Find the time at which the coin hits the water.
3
The height of a projectile is modeled by the equation y=­2x2 + 38x + 10, where x is time, in seconds, and y is height, in feet. During what interval of time, to the nearest tenth of a second, is the projectile at least 125 feet above ground?
4
The weekly profit function in dollars of a small business that produces fruit jams is P(x) = ­0.4x2 + 40x ­ 360 where x is the number of jars of jam produced and sold.
a) Find the number of jars of jam that should be produced to maximize the weekly profit
b)
Find the maximum profit
c) How many jars need to be sold in order to make a profit
5
During archer practice, Paula shoots an arrow into the air such that its height at any time t, is given by the function h(t) = ­16t2 + kt + 5. If the maximum height of the arrow occurs at time t=3.5 seconds, what is the value of k?
6
Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is represented by the equation L = ­5t2 ­ 8t +120, where L represents the number of liters of water in the bathtub and t represents the number of time, in minutes, since the plug was pulled.
How many liters of water were in the bathtub when Barb pulled the plug?
Determine, to the nearest tenth of a minute, the amount of time it takes for all the water in the bathtub to drain.
7
The path of a rocket fired during a fireworks display is given by the equation s(t) = 64t ­ 16t2, where t is the time, in seconds, and s is the height, in feet. What is the maximum height, in feet, the rocket will reach? In how many seconds will the rocket hit the ground?
8
A laundry owner’s estimate of her weekly profits, p, in dollars, is given by the equation p = ­4w2 + 160w, where w represents the number of workers she hires.
What is the number of workers she should hire in order to earn the greatest profit?
9
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