A ball is thrown straight up in the air at a velocity of 100 feet per second. The height of the ball at t seconds
is given by the formula: h = 100t – 5t^2 Find the
maximum height of the ball and when it will land. Maximum Height ft. Land after: ___ seconds

Maximum height = 500 feet

Land after = 20 seconds

Step-by-step explanation:

Let us follow the movement of the ball as it is thrown upwards.  We notice that we get to a point, where the change in the height of the ball with respect to time becomes = 0. This means that the ball is at its maximum position.

Hence, mathematically, at maximum height,

Recall,

From our problem, we can also deduce that at the maximum height, the velocity of the ball is = 0. i.e

hence,

The time the ball takes to reach a maximum height is 10 seconds.

The next step will be to substitute this time value into the equation for the height.

The maximum height is 500 feet

The object will land after t X 2 seconds = 10 X 2 = 20 seconds. This is because it will have to go up and come back down. This should take twice the time.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

thats one

step-by-step explanation: