# Numerical Problem for motion along a plane (HELP) -2-

• May 26th 2009, 03:09 AM
mj.alawami
Numerical Problem for motion along a plane (HELP) -2-
Question:
A stone is throws with an initial horizontal velocity of 10m/s form the top of a tower 200m high.
a)where is the stone 2 seconds after being thrown?
b)when will it hit the ground?
c)what is the speed upon hitting the ground?

Attempt:
a)20m
b)20s
c)10m/s
• May 26th 2009, 09:41 AM
earboth
Quote:

Originally Posted by mj.alawami
Question:
A stone is throws with an initial horizontal velocity of 10m/s form the top of a tower 200m high.
a)where is the stone 2 seconds after being thrown?
b)when will it hit the ground?
c)what is the speed upon hitting the ground?

Attempt:
a)20m
b)20s
c)10m/s

Let t denote the time measured in seconds. $\displaystyle g = 9.81\ \dfrac m{s^2}$ is the gravitational acceleration(?).

The path of the stone is described by two independent movements: a horizontal and a vertical:

$\displaystyle \left|\begin{array}{l}x(t)=10 \cdot t\\y(t)=200-\dfrac12 \cdot g \cdot t^2\end{array}\right.$

to a): Plug in t = 2 into both equations to get (20, 180.38)

to b): The stone reaches the ground when y(t) = 0. Solve for t. (I've got t = 6.3855 s)

to c) The total speed is calculated by $\displaystyle v = \sqrt{(x'(t))^2+(y'(t))^2}$
Plug in t = 6.3855. I've got $\displaystyle v = 63.435\ \dfrac ms$