Football hangtime

on3winyoureyes

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Jon punts the football from ground level, its distance above the ground is given by d(t)=70t-16t^2, d(t) is in feet and t is in seconds

a. use definition of derivative as difference quotient of function d.
I already did that and got 70-32a or 70-32t (I used (f(a+h)-f(a))/h))

b. Find the equation of the line tangent to the graph of f at the point where t=3
I'm sure if I got this right but I got y=-26x+144
by doing y-66=-26(x-3)

c. Neglecting air resistance, how long will the ball be in the air? (known as hang time)
This, I have no idea.
 
Jon punts the football from ground level, its distance above the ground is given by d(t)=70t-16t^2, d(t) is in feet and t is in seconds

a. use definition of derivative as difference quotient of function d.
I already did that and got 70-32a or 70-32t (I used (f(a+h)-f(a))/h))

b. Find the equation of the line tangent to the graph of f at the point where t=3
I'm sure if I got this right but I got y=-26x+144
by doing y-66=-26(x-3)

c. Neglecting air resistance, how long will the ball be in the air? (known as hang time)
This, I have no idea.
I agree with parts (a) and (b). For part (c), the ball is on the ground at time t=0, i.e. d(0)=0. At what other time is d(t) equal to zero. That is, what are the solutions to
d(t) = 70 t - 16 t2 = 0.

BTW: I have found that derived equations, i.e. the straight line of (b), generally keep the same independent variables as the initial equation, i.e. the straight line would be written as y=-26t+144. However, your answer is not incorrect.
 
Jon punts the football from ground level, its distance above the ground is given by d(t)=70t-16t^2, d(t) is in feet and t is in seconds

c. Neglecting air resistance, how long will the ball be in the air? (known as hang time)
This, I have no idea.
This works the same in your calculus class as it did back in your algebra class. You've been given an equation for the height d above ground at time t. You've been given a height of d = 0 ("no longer in the air" means "back on the ground"), and have been asked to solve the quadratic equation for the value of t. Factoring should get you to the answer. ;)
 
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