How do I solve this? Please give me a simple explanation thank you!

# r=1/32v_osin2θ.# This is what the equation looks like.
A batted baseball leaves the bat at an angle of θ with the horizontal and an initial velocity of v0=100 feet per second. The ball is caught by an outfielder 300 feet from home plate. Find θ if the range r of a projectile is given by r=1/32vsin2θ.

1 Answer
Feb 15, 2018

You cannot solve this equation with the given values.


Well, you are given all the "ingredients" to solve the equation for theta, so let's get to it!
The last part of the question says "the range r of a projectile is given by #r=1/32 v_0 sin 2theta#".
What is the range in our case? Yes, 300 feet.
So you replace #r# by 300 (feet).
What is #v_0#? Yes, 100 feet per second.
So you replace #v_0# by 100 (feet per second).

We now have:
#300 = 1/32 100 sin 2theta#
(of course, this is not a very good physics question as you should really care about how the units all carry out, but we'll ignore them in this case as the formula is given to us as such and is not the point of this exercise).

Shuffling around the terms, we get:
#sin 2theta = 96#
This is impossible, since the sine of an angle is always between -1 and 1.
Therefore, you cannot solve this equation with these input values.
That is, either the equation is wrong, or the input values are wrong.

Hope this helps!