A golf ball is hit in the air. The path of the golf ball is modelled by the relation h=-5t^2+20t where h is th?

h(t) = 20t - 5t²

A) h(1) = 15 metres

B) 20t - 5t² = 0

=> 5t(4 - t) = 0

i.e. ball at ground level when t = 0 and t = 4 seconds

C) The maximum height is attained mid-flight, so at 2 seconds

=> h(2) = 20(2) - 5(2)²

i.e. 20 metres

or, v = dh/dt = 20 - 10t

v = 0 at maximum height

=> 20 - 10t = 0

i.e. at t = 2 seconds

Here is a sketch of the ball's trajectory:

http://www.wolframalpha.com/input/?i=y+%3D+20x+-+5...

:)>

You have the function h(t) = -5t^2 + 20t for the position of the golf ball.

A. Just plug in 1 second.

h(1) = -5(1)^2 + 20(1) = -5 + 20 = 15 meters

B. When the ball hits the ground, its position is 0. Therefore, we equate h to 0 and get its zeroes.

-5t^2 + 20t = 0

t(-5t + 20) = 0

t = 0 and t = 4

We take t = 4 seconds.

C. The ball is at its max height when the velocity is equal to zero. To get the velocity, get the first derivative of h(t). The derivative is h'(t) = v(t) = -10t + 20. Now, equate this to zero.

-10t + 20 = 0

20 = 10 t

2 seconds = t

Since you're asked for the max height, plug in the value to your h(x).

h(2) = -5(2)^2 + 20(2) = -20 + 40 = 20 meters

A) Replace t by 1:

-5 + 20 = 15

The height of the ball after one second is 15m

B) The ball is on the ground when the height is zero:

-5t(t - 4) = 0

The zero's are x = 0 and x = 4, since at zero seconds, the ball didn't even leave the ground, the answer must be 4 seconds.

C) Take the derivative of the function:

-10t + 20 = 0

t = 2

Replace the t's of the original equation by 2:

-5(2)^2 + 20(2) = 20m

Hope this helped!

The measure of the membership determines the degree or attitude the ball comes off of the face of the club - the length of the club creates a swing arc that determines the power of the swing - a pitching wedge which has a traditional loft of 48* can also be hit one hundred twenty five yards - should you choke all the way down to the metallic on the same 48* membership, the ball will go about 20-25 yards shorter - the longer the club, the longer the swing arc which produces more vigour delivered in to the ball - that is why you see the clubs get step by step longer because the measure of the membership lessens which allows you to hit the ball farther and scale down with every club down the line - in your illustration, a 2 iron is about 1 inch longer and about 2-four levels less than a 3 iron which is why that you would be able to hit the two iron farther than the 3 iron