# Hero velocity problem

• Oct 9th 2012, 04:10 PM
Oldspice1212
Hero velocity problem
In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 86.0 km/h, to his enemy's car, which is going 103km/h . The enemy's car is 14.5m in front of the hero's when he lets go of the grenade.

If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 degrees above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

Find the magnitude of the velocity relative to the earth.

• Oct 9th 2012, 04:35 PM
skeeter
Re: Hero velocity problem
let $\displaystyle t$ = time (in sec) the grenade is a projectile

position of the enemy car in meters ...

$\displaystyle x = 14.5 + \frac{515}{18} \cdot t$

position of the projectile ...

$\displaystyle x = \left(v_x + \frac{215}{9}\right)t$

... where $\displaystyle v_x$ is the x-component of grenade's initial velocity

since the idea is for the projectile and enemy car to be at the same place at the same time ...

$\displaystyle \left(v_x + \frac{215}{9}\right)t = 14.5 + \frac{515}{18} \cdot t$

in the y-direction, the projectile's total displacement is zero ...

$\displaystyle 0 = v_y t - \frac{1}{2}gt^2$

... where $\displaystyle v_y$ is the y-component of the grenade's initial velocity.

solving for $\displaystyle t$ ...

$\displaystyle t = \frac{2v_y}{g}$

since the launch angle is $\displaystyle 45^\circ$ , $\displaystyle v_y = v_ x$ , so $\displaystyle t = \frac{2v_x}{g}$.

... substitute for $\displaystyle t$ in the equal position equations and solve for $\displaystyle v_x$
• Oct 9th 2012, 04:44 PM
Oldspice1212
Re: Hero velocity problem
If vy=vx wouldn't vx be 0 then?
• Oct 9th 2012, 04:47 PM
skeeter
Re: Hero velocity problem
Quote:

Originally Posted by Oldspice1212
If vy=vx wouldn't vx be 0 then?

how did you arrive at that conclusion?
• Oct 9th 2012, 04:56 PM
Oldspice1212
Re: Hero velocity problem
I have no clue what I'm doing :(. How do you get the relative velocity?!
• Oct 9th 2012, 05:07 PM
skeeter
Re: Hero velocity problem
Quote:

If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 degrees above the horizontal, what should the magnitude of the initial velocity be?

I've set up the necessary equations for you to solve for the magnitude of the grenade's initial velocity. If you cannot follow the proposed solution, then I advise you have a face-to-face consultation with your instructor.
• Oct 9th 2012, 05:18 PM
Oldspice1212
Re: Hero velocity problem
I got it now, thanks :d
• Oct 9th 2012, 07:00 PM
Oldspice1212
Re: Hero velocity problem
Thought I had it, guess not, I got 54.7 km/h?