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lbvjy [14]
3 years ago
15

A small rubber ball is launched by a compressed-air cannon from ground level with an initial speed of 17.3 m/s directly upward.

Choose upward as the positive direction in your analysis. (a) What is the maximum height above the ground that the ball reaches?
Physics
1 answer:
elena-s [515]3 years ago
7 0

Answer:

h=15.27m

Explanation:

Since at maximum height the vertical velocity must be null it's better to use the formula:

v_f^2=v_i^2+2ad

We will use this formula for the vertical direction, choosing the upward direction as the positive one, so we have:

0=v_i^2+2ah

or

h=-\frac{v_i^2}{2a}

which for our values is:

h=-\frac{(17.3m/s)^2}{2(-9.8m/s^2)}=15.27m

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"Fig is attacted with answer"

Answer:

a) d = 33.72 m

b) v_{i} = 26 m/s

c) β = 71.08°

Explanation:

a)

When an object is thrown into the air under the effect of the gravitational force, the movement of the projectile is observed. Then it can be considered as two separate motions, horizontal motion and vertical motion. Both motions are different, so that they can be handled independently.

Given data:

time = t = 4.00 s

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Angle = θ = 60°

Horizontal distance = d = ?

Using 2nd  equation of motion

h = v_{y_{f}}t + \frac{1}{2}gt^{2}

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This is vertical component of velocity when the ball is on the roof. To calculate the Final velocity and horizontal component, we use

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v_{x_{f}} = v_{f}cosθ

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b)

We know the values of Landing angle, height of roof, time of flight. In part a, We calculate the landing velocity of the ball and also its horizontal and vertical component. As the ball followed the projectile path, and we know that in projectile motion the horizontal component of the velocity remain constant throughout his motion. So there is no acceleration along horizontal path.

So,

v_{x_{f}} = v_{x_{i}}

but the vertical component of velocity vary with and there is an acceleration along vertical direction which is equal to gravitation acceleration g.

So,

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9.8 =  14.6 - v_{y_{i}}) / 4

v_{y_{i}} = 24.6 m/s

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v_{i} = \sqrt{8.43^{2}+24.6^{2}}

v_{i} = 26 m/s

c)

cos β = v_{x_{i}} / v_{i}

β = cos⁻¹ (8.43 / 26)

β = 71.08°

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