A Ball Is Given An Initial Velocity Of 10.0 M/S At 37\Xb0 Above The Horizontal., "(A) Calculate The Horizontal And Vertical Components Of The Balls In

A Ball Is Given An Initial Velocity Of 10.0 M/S At 37\Xb0 Above The Horizontal., "(A) Calculate The Horizontal And Vertical Components Of The Balls In

A ball is given an initial velocity of 10.0 m/s at 37° above the horizontal.

(a) Calculate the horizontal and vertical components of the balls initial velocity. (b) Calculate the horizontal and vertical displacements (dx and dy) of the ball after 1.5 seconds.
(c) Calculate the horizontal and vertical components of the velocity of the ball after 1.5 seconds.

a) vertical component of initial velocity

$u_{x}= u cos\theta$

$u_{x}= 10\times cos37$

$u_{x}= 10\times\frac{4}{5}=8m/s$

Horizontal component of velocity.

$u_{y}= u sin\theta$

$u_{y}= 10\times sin37$

$u_{y}= 10\times\frac{3}{5}=6m/s$

b) vertical displacement.

$x= (u_{x})t$

$u_{x}= (8)\times1.5=12m$

Horizontal displacement.

$y=u_{y}t-\frac{1}{2}gt^{2}$

$y=(6\times1.5)-\frac{1}{2}\times(1.5)^{2}$

$y=9-11.25=-2.25m$

c) Vertical component of velocity is independent of time.

So, $v_{x}=u_{x}= 8 m/s$

Horizontal component at t=1.5s

$v_{y}=u_{y}-gt$

$v_{y}=6-(10\times1.5)=-9m/s$

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