During halftime of a soccer game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 64 feet per second. The T-shirt is caught 50 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
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Part 1
The T-shirt takes
enter your response here second(s) to reach its maximum height.
(Type an integer or a decimal.)
The T-shirt will take 1 second to reach its maximum height.
inccorect
I apologize for the mistake. To find out how long it will take for the t-shirt to reach its maximum height, we can use the formula:
Time to reach maximum height = Initial velocity / (acceleration due to gravity)
Given:
Initial velocity = 64 ft/s (upward)
Acceleration due to gravity = -32 ft/s^2 (it's negative because gravity acts downward)
Time to reach maximum height = 64 ft/s / 32 ft/s^2 = 2 seconds
So, the T-shirt will take 2 seconds to reach its maximum height.
During halftime of a soccer game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 64 feet per second. The T-shirt is caught 50 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time?
Question content area bottom
Part 1
The T-shirt takes
2 second(s) to reach its maximum height.
(Type an integer or a decimal.)
Part 2
The T-shirt's maximum height is
enter your response here feet above the field.
(Type an integer or a decimal.)
Part 1:
We have calculated that the T-shirt takes 2 seconds to reach its maximum height.
Part 2:
To find the maximum height, we can use the kinematic equation:
h(t) = h0 + v0t - 16t^2
where:
h(t) is the height of the T-shirt at time t
h0 is the initial height = 4 ft
v0 is the initial upward velocity = 64 ft/s
t is the time
At the maximum height, the velocity is zero. This means that v0 - 32t = 0
Solving for t, we get:
t = v0 / 32
t = 64 / 32
t = 2 seconds
Now, substitute t = 2 into the height equation:
h(2) = 4 + 64(2) - 16(2)^2
h(2) = 4 + 128 - 64
h(2) = 68 ft
Therefore, the T-shirt's maximum height is 68 feet above the field.