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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.

Respuesta :

jorgezarate

Answer:

[tex]t=d/(v_{o}*cos(\alpha ))[/tex]

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

Explanation:

Kinematics equation in the axis X:

[tex]x=v_{o}*cos(\alpha )*t[/tex]

The projectile strikes the building at time t:

[tex]d=v_{o}*cos(\alpha )*t[/tex]

[tex]t=d/(v_{o}*cos(\alpha ))[/tex]  (1)

Kinematics equation in the axis Y:

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

We replace (1) in (2):

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

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

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