# Thread: Calculus 3 - Range and Height Problem

1. ## Calculus 3 - Range and Height Problem

A shot leaves a thrower's hand 6.5 feet above the ground. The angle at which it was thrown is 45 degrees and it had a velocity of 44 $\frac{ft}{s}$. Find the time it hits the ground and the range.

The equations are as follows:

$x=x_o + (V_o cos\theta)t$ ; $y=y_o + (V_o tsin\theta - \frac{1}{2} gt^2)$

So basically what I have to do is, set the y equation equal to t and find a t value. Then plug that t value in for the x equation. Here's my work

$y=(\frac{-g}{2})t^2 + (V_o sin\theta)t + y_o$ which is in $(At^2 + Bt + C = 0)$ format.

$t=\frac{V_o sin\theta + \sqrt{(V_o sin\theta)^2 + 2gy_o}}{g}$

Subbed my values in and I got t=2.1348 s

Plugged that value for t in the x equation and got 66.4194 ft. How does my equation look for finding t? If its right then I think I can assume my values for t and x are correct as well.

2. Originally Posted by VitaX
A shot leaves a thrower's hand 6.5 feet above the ground. The angle at which it was thrown is 45 degrees and it had a velocity of 44 $\frac{ft}{s}$. Find the time it hits the ground and the range.

The equations are as follows:

$x=x_o + (V_o cos\theta)t$ ; $y=y_o + (V_o tsin\theta - \frac{1}{2} gt^2)$

So basically what I have to do is, set the y equation equal to t and find a t value. Then plug that t value in for the x equation.
That is not in English, what you do is you solve for when the height is zero:

$y_o + (V_0\, t \sin(\theta) - \frac{1}{2} gt^2)=0$

for $t$, this is a quadratic in $t$ and so has two roots, you need the positive one (which is what you have found).

Here's my work

$y=(\frac{-g}{2})t^2 + (V_o sin\theta)t + y_o$ which is in $(At^2 + Bt + C = 0)$ format.

$t=\frac{V_o sin\theta + \sqrt{(V_o sin\theta)^2 + 2gy_o}}{g}$

Subbed my values in and I got t=2.1348 s

Plugged that value for t in the x equation and got 66.4194 ft. How does my equation look for finding t? If its right then I think I can assume my values for t and x are correct as well.
The final answer is OK, but you give too many significant digits (only 5 are justified)

CB

3. Just a typo. Meant to say set y equation equal to zero.