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11111nata11111 [884]
2 years ago
8

During a race the dirt bike was observed to leap up off the small hill at A at an angle of 60^o with the horizontal. If the poin

t of landing is 20 ft away, determine the approximate speed at which the bike was traveling just before it left the ground. Neglect the size of the bike for the calculation.
Physics
1 answer:
const2013 [10]2 years ago
8 0

Answer:

Velocity is equal to 27.3 feet per second  and time is equal to 1.4668 seconds

Explanation:

Given

The horizontal distance traveled by  dirt bike before landing = 20 feet

Angle of flight = 60 degree

As we know that Horizontal distance (H) is equal to

= H_0 + V_0 * t\\

Where H_0 is the initial horizontal distance

V_0 is the velocity with which the bike is travelling in horizontal direction

and t is the time in seconds

Substituting the given values, we get -

H = H_0 + v*t\\20 = 0 + v * cos \theta * t\\20 = v * cos 60 * t\\t = \frac{20}{v * cos 60} \\t = \frac{40}{v}

Now distance traveled in vertical direction is equal to

Y = Y_0 + v_0 * t + \frac{1}{2} a * t^2

here acceleration will be equal to acceleration due to gravity which is equal to - 32.2 \frac{ft}{s^2}. It is negative as its is acting in upward direction

Thus,

Y = 0 + v * sin 60 + \frac{1}{2}  * (-32.2) * (\frac{40}{v} )^2\\0 = 0  + 0.866 v + \frac{-25760}{v^2} \\0.866 v = \frac{-25760}{v^2}\\v^3 = \frac{-25760}{0.866} \\v = 27.3

Velocity is equal to 27.3 feet per second  and time is equal to 1.4668 seconds

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a)

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b)

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Explanation:

a)

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v_{o} = initial speed of asteroid = 7600 m/s

v = final speed of asteroid = 5000 m/s

W = Work done by the force on asteroid

Using work-change in kinetic energy theorem

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