Question

A projectile is fired at t = 0 with an initial velocity ofvi at an angle of θ with respectto the horizontal towards the vertical side of a building that is adistance d away as shown in the figure.
(a) Determine an equation for the time at which the projectilestrikes the building, in terms of the quantities d, v_i, theta, andg.


(b) Determine an equation for the height h above theground at which the projectile strikes the building, in terms ofthe quantities d, v_i, theta, and g.

Answer 1

Answer:

$t=d/(v_{o}*cos(\alpha ))$

$y =d*tan(\alpha )- 1/2*g^{2}d^{2}/(v_{o}^{2}*(cos(\alpha ))^2)$

Explanation:

Kinematics equation in the axis X:

$x=v_{o}*cos(\alpha )*t$

The projectile strikes the building at time t:

$d=v_{o}*cos(\alpha )*t$

$t=d/(v_{o}*cos(\alpha ))$  (1)

Kinematics equation in the axis Y:

$y =v_{o}*sin(\alpha )*t - 1/2*gt^{2}$  (2)

We replace (1) in (2):

$y =v_{o}*sin(\alpha )*d/(v_{o}*cos(\alpha )) - 1/2*g(d/(v_{o}*cos(\alpha )))^{2}$  

$y =d*tan(\alpha )- 1/2*g^{2}d^{2}/(v_{o}^{2}*(cos(\alpha ))^2)$  (2)