horizontal distance: 27=vo*cosTheta*time
vertical distance:
hf=Hi+vo*sinTheta*time-4.8t^2
you know hf, ho.
solve for time in the first equation in terms of vo, Theta (50deg).
put that into the second equation for time, then solve for vo. You may have to solve a quadratic equation.
Hello! I'm having a bit of trouble trying to solve this physics problem. I'm not sure which equations to use or where or how to plug my variables:
Robin Hood wishes to shoot an arrow through the open window of a tall castle wall. The window is 16m meters above the ground and Robinhood stands 27 meters from the base of the tower. If he aims the arrow (with note attached) at an angle of 50º above the horizontal, with what velocity must he fire the arrow in order for it to enter the window? (assume it enters Maid Marian’s room at the top of the arrows path and she is out of the way)
Thank you!
6 answers
the vertical and horizontal times of flight must be the same for the windows position
... 27 m horizontal, and 16 m vertical
horizontal time ... distance / velocity ... t = 27 m / v cos(50º)
vertical time ... 16 m = 1/2 g t^2 + v sin(50º) t ... 0 = 4.9 t^2 + [v sin(50º) t] - 16
use the quadratic formula to solve for t in the vertical equation (it will be in terms of v)
set the two t's equal (horizontal and vertical), and solve for v
... 27 m horizontal, and 16 m vertical
horizontal time ... distance / velocity ... t = 27 m / v cos(50º)
vertical time ... 16 m = 1/2 g t^2 + v sin(50º) t ... 0 = 4.9 t^2 + [v sin(50º) t] - 16
use the quadratic formula to solve for t in the vertical equation (it will be in terms of v)
set the two t's equal (horizontal and vertical), and solve for v
I think Scott meant to include a negative sign with g.
how exactly do I use the quadratic formula here? like where would I insert the variables to solve
thanks for catching that, Bob
a = - 4.9 , b = v sin(50º) , c = -16
t = {-b ± √[b^2 - (4 a c)]} / (2 a)
a = - 4.9 , b = v sin(50º) , c = -16
t = {-b ± √[b^2 - (4 a c)]} / (2 a)
Y^2 = Yo^2 + 2g*h = 0.
Yo^2 + (-19.6)16 = 0,
Yo^2 = 313.6
Yo = 17.71 m. = Ver. component of initial velocity.
Yo = Vo*sin50 = 17.71m.
Vo = 23.12m/s[50o].
Yo^2 + (-19.6)16 = 0,
Yo^2 = 313.6
Yo = 17.71 m. = Ver. component of initial velocity.
Yo = Vo*sin50 = 17.71m.
Vo = 23.12m/s[50o].