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3 years ago

Vector B~ has x, y, and z components of 8.7,

Physics

1 answer:

blagie [28]3 years ago

3 0

Answer:

The magnitude of B is $10.95\ units$

Explanation:

we know that

The magnitude of Vector B is

$B=\sqrt{x^{2}+y^{2}+z^{2}}$

where

x,y and z are the components of vector B

we have

$x=8.7\ units, y=1.4\ units,z=6,5\ units$

substitute

$B=\sqrt{8.7^{2}+1.4^{2}+6.5^{2}}$

$B=\sqrt{119.9}$

$B=10.95\ units$

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$v_{y,f}=\left(20.5\dfrac{\rm m}{\rm s}\right)\sin(-38^\circ)\approx-12.6\dfrac{\rm m}{\rm s}$

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$x=v_{x,i}t=v_{x,f}t$

It lands 103 m away from where it's hit, so we can determine the time it it spends in the air:

$103\,\mathrm m=\left(16.2\dfrac{\rm m}{\rm s}\right)t\implies t\approx6.38\,\mathrm s$

The vertical component of the ball's velocity at time t is

$v_{y,f}=v_{y,i}-gt$

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which carries an initial speed of

$\|\mathbf v_i\|=\sqrt{{v_{x,i}}^2+{v_{y,i}}^2}\approx\boxed{52.4\dfrac{\rm m}{\rm s}}$

and direction θ such that

$\tan\theta=\dfrac{v_{y,i}}{v_{x,i}}\implies\theta\approx\boxed{72.0^\circ}$

(b) I assume you're supposed to find the height of the ball when it lands in the seats. The ball's height y at time t is

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so that when it lands in the seats at t ≈ 6.38 s, it has a height of

$y=\left(49.9\dfrac{\rm m}{\rm s}\right)(6.38\,\mathrm s)-\dfrac12\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(6.38\,\mathrm s)^2\approx\boxed{119\,\mathrm m}$

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3 years ago