# Projectile Angle and Distance problem

## Homework Statement

A projectile was launched from the top of a 100m tower upward at an angle theta to the horizontal with an initial velocity of 36m/s. The time of flight of the projectile was 8 seconds.

Determine:
i) The angle of projection
ii) The maximum height reached by the projectile

S=ut+1/2at^2

## The Attempt at a Solution

I am used to solving these questions when i am not given time but given both the horizontal and vertical distances. At which I use the quadratic formula to solve for theta. However in this case I can not do that as when i split my horizontal and vertical components and apply the above equations I am left with these.

Horizontally
S=36cos(?)*8

Vertically
-100=36sin(?)*8+0.5*-9.81*64

I have tried rearranging the vertical formulas to solve for theta

-1/2*-9.81*64-100/8=36sin(?)
301.42 = 36*sin(?)
sin-1(36/301.42) = 6.85 degrees

I really don't think that the answer is correct. The lecture who set the question will not give any answers.

TSny
Homework Helper
Gold Member
Vertically
-100=36sin(?)*8+0.5*-9.81*64
OK

I have tried rearranging the vertical formulas to solve for theta

-1/2*-9.81*64-100/8=36sin(?)
You have only the 100 being divided by 8. But is that correct?

Yeah. Only the 100 divided by 8. Im thinking that maybe 6.85 degrees is the correct angle for a projectile to fall from 100 metres in 8 seconds.

TSny
Homework Helper
Gold Member
Only the 100 divided by 8.
Check the algebra on this. I don't think it's correct to have just the 100 divided by 8.

Im not exactly sure on the rerrangment to solve for U. As i thought my 1st rearrange was correct.

I tried the rearrange dividing the whole thing by 8 = sin-1(26.74/36) = 47.96 degrees.

I tried the rearrange dividing by 16 from 1/2*8 under everything = sin-1(36/60.76) = 36.33 degrees

s = ut + 1/2at^2
ut = s - 1/2at^2
u = (s - 1/2at^2)/t
36sin(?) = (-100-1/2*-9.81*64)/8

Sin(?)= 26.74/36
Sin-1(26.74/36) = (?)

TSny
Homework Helper
Gold Member
s = ut + 1/2at^2
ut = s - 1/2at^2
u = (s - 1/2at^2)/t
36sin(?) = (-100-1/2*-9.81*64)/8

Sin(?)= 26.74/36
Sin-1(26.74/36) = (?)
That looks correct.