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

`t=d/(v_(o)*cos(\alpha ))`

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

Step-by-step 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)