Asap 1. find the time it takes for a rocket following the path of the parametric equations, x = 4t - 8 and y = -2t^2 + 18, to hit the ground. 2. find the time it takes for a ball following the path of the parametric equations, x = 4t - 8 and y = -t^2 + 18t, to reach a maximum. if you have the time to me with a few different type of problems that i don't understand i would be very grateful : )

                                                Question 1

A rocket is said to be following the path described by the parametric equations below.

It is worth noting that  equation (1) represents the horizontal motion of the rocket and equation (2) represents the vertical motion of the rocket. Also worth noting is that the motion in the two directions is independent of each other.

To determine the time it takes for the rocket to hit the ground, we have to set equation (2) to be equal to zero, because that represents a height of zero, i.e when the rocket hits the ground.

The only value that makes sense is .

                                                 Question 2

A ball is said to be following the path described by the parametric equations below,

The ball reaches a maximum in the -direction, which is the only direction we will concern ourselves with in this problem. The motion in the -direction is parabolic represented by equation (4) with . To get the time when the ball is at a  maximum height, we have to use the formula for finding the coordinate of the maximum,

The ball will have a maximum height at 9 seconds.

Another way to determine the maximum height would be to take the derivative of The derivative of  equation (4) is  . The maximum value of occurs when the derivative is zero, i.e

y=x+2 hope this jdjxhdnzbdjdo

10cm

step-by-step explanation:

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