A golf ball is hit with an initial velocity of 50 m/s at an angle of 45° above the horizontal. How long will the golf ball be in the air?



A)
3.6 s

B)
5.4 s

C)
7.2 s

D)
8.8 s

Respuesta :

The vertical component of its initial velocity is

[tex]v_{0y}=\|\mathbf v_0\|\sin45^\circ=35\,\dfrac{\mathrm m}{\mathrm s}[/tex]

Its height above the ground at time [tex]t[/tex] is given by

[tex]y=v_{0y}t-\dfrac g2t^2[/tex]

where [tex]g=9.8\,\frac{\mathrm m}{\mathrm s}[/tex] is the acceleration due to gravity. The ball reaches the ground when [tex]y=0[/tex], so for [tex]t>0[/tex] this occurs at

[tex]0\,\mathrm m=\left(35\,\dfrac{\mathrm m}{\mathrm s}\right)t-\dfrac12\left(9.8\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2[/tex]

[tex]\implies t=7.1\,\mathrm s[/tex]

which makes B the most likely to be correct.

aachen

Answer:

[tex]7.21 sec[/tex]

Explanation:

In this question the ball is doing projectile motion.

Given:

Initial velocity, [tex]v_i=50\ m/s.[/tex]

Angle from horizon, [tex]\theta=45^o.[/tex]

Time taken to reach the ground or time in which it was on air is given by:

[tex]T=\dfrac{2\times v\times sin\theta}{g}[/tex]

where g is acceleration due to gravity= [tex]9.8 \ m/s^2[/tex].  

Putting values in above equation we get.

[tex]T=\dfrac{2\times 50\times sin45^o}{9.8}=7.21 \ sec.[/tex]

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