A football is punted into the air and it's height is given by the equation, h(t)=-4.9t^2 + 24.5t + 1
a)how high is it after 1 second?
b)how long does it take to reach it's max height?
c)what is it's max height?
d)how long does it take to hit the ground?
koochie
I hate henry get out of here henry
To answer these questions, we can use the given equation for the height of the football:
h(t) = -4.9t^2 + 24.5t + 1
a) To find the height after 1 second, we substitute t = 1 into the equation:
h(1) = -4.9(1)^2 + 24.5(1) + 1
Calculating this expression gives us the height after 1 second.
b) The maximum height is achieved when the football reaches its peak before descending. To find the time it takes to reach the maximum height, we need to determine the value of t when the derivative of the equation is zero.
The derivative of the equation h(t) is given by:
h'(t) = -9.8t + 24.5
Setting h'(t) equal to zero and solving for t will give us the time at which the football reaches its maximum height.
c) The maximum height can be calculated by substituting the value of t obtained in step b into the equation:
h(t_max) = -4.9(t_max)^2 + 24.5(t_max) + 1
Computing this expression will give us the maximum height.
d) To find how long it takes for the football to hit the ground, we need to determine the time when the height is zero. So, we set h(t) equal to zero and solve for t:
-4.9t^2 + 24.5t + 1 = 0
Solving this quadratic equation will give us the time it takes for the football to hit the ground.
In summary:
a) Substitute t = 1 into the equation to find the height after 1 second.
b) Set the derivative of h(t) equal to zero and solve for t to find the time it takes to reach the maximum height.
c) Substitute the time obtained in step b into the equation to find the maximum height.
d) Solve the quadratic equation h(t) = 0 to find the time it takes for the football to hit the ground.
A football is punted into the air. Its heighth, in meters, aftert seconds is given by the equationh = −4.9t2 + 24.5t + 1.
a. h = -4.9*1^2 + 24.5*1 + 1.
b. Y = Yo + g*Tr = 0 at max h.
Tr = -Yo/g = -24.5/-9.8 = 2.5 s. = Rise
time or time to reach max h.
c. h max = -4.9Tr^2 + 24.5Tr + 1
d. h max = 0.5g*Tf^2
Tf = ?.
T = Tr + Tf.