Ball caught by player, solve quadratic equation

[kitkat87]

Homework Statement

First part of the question (SOLVED)

A football player kicks a football so that the angle of incidence is 50 DEG and the initial magnitude of velocity of the ball is 15 m/s.

Find the:
a) Balls maximum height = 6.7 m
b) Time of flight = 2.3 s
c) time when the ball reaches the maximum height = 1.2 s
d) horizontal distance = 23 m
e) velocity at impact = 15 m/s [50 DEG below horizontal]

Second part of the question (Need help)

Now imagine that the situation is exactly the same, except this time, the ball is caught by a player when it is at a height of 1.5 m above the ground. Determine the horizontal range of the ball, the length of time that it was in the air, and the final velocity.

2. The attempt at a solution

Let [up] be the positive y-direction and [forward] be the positive x-direction.

Vertically
V1y = +11.49 m.s
Ay = -9.8 m/s
Total y displacement = 1.5m

Using the vertical component to find time:

Displacement y = V1y (change in time) + 1/2 Ay (change in time)^2
1.5 m = (+11.49 m/s)(change in time) + 1/2 (-9.8 m/s^2)(change in time)^2

There is a quadratic equation to solve in this equation so it has been rearranged

(9.8 m/s^2)(change in time)^2 + (-11.49 m/s)(change in time) + 1.5m = 0

Now my workbook gives the rearrangement differently but doesn't explain why and this is where I need help.

My workbook says the rearrangement should look like this:

(4.9 m/s^2)(change in time)^2 + (-11.49 m/s)(change in time) + 1.5m = 0

Can someone please explain why the acceleration was divided in two?

 

[Doc Al]

Displacement y = V1y (change in time) + 1/2 Ay (change in time)^2

See the factor of 1/2? That's what you lost.

Can someone please explain why the acceleration was divided in two?

That factor of 1/2 is from the kinematic formula for displacement. You must have dropped it and not noticed when you did your rearrangement.