Question

A cyclist going up a slope with angle of 30 with speed of 3.5 m/s. If he stop pedalling how much distance will he move before coming to rest friction is negligible Solve it please

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Distance\:travelled=1.225\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: velocity(u) = 3.5 \: m/s \\ \\ \tt: \implies Angle \: of \: inclination ( \theta)= 30 \degree \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Distance \: travelled = ?$

• According to given question :

$\tt \circ \: Final \: velocity = 0 \: m/s \\ \\ \tt \circ \: Downward \: acceleration = g \: sin \: \theta\:m/s^{2} \\ \\ \tt \circ \: Initial \: velocity = 3.5 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {v }^{2} = {u}^{2} +2as \\ \\ \tt: \implies {0}^{2} = {(3.5)}^{2} + 2 \times ( - g \: sin \: \theta) \times s \\ \\ \tt: \implies 0 = 12.25 - 2 \times 10 \times sin \: 30 \degree \times s \\ \\ \tt: \implies - 12.25 = - 2 \times 10 \times \frac{1}{2} \times s \\ \\ \tt: \implies \frac{ - 12.25}{ - 10} = s \\ \\ \green{\tt: \implies s = 1.225 \: m} \\ \\ \green{\tt \therefore Distance \: travelled \: is \: 1.225 \: m}$

Answer 2

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QUESTION -

A cyclist going up a slope with angle of 30 with speed of 3.5 m/s.

If he stops pedalling how much distance will he move before coming to rest friction is negligible .

Solve it please.......

SOLUTION -

In the above Question, the following information is given....

A cyclist going up a slope with angle of 30 with speed of 3.5 m/s.

If he stops pedalling how much distance will he move before coming to rest friction is negligible .

This can be easily solved by using the third Equation of Motion ....

According to the Equation :

{ V } ^ 2 = { U } ^ 2 + 2AS

=> { 0 } ^ 2 = { 3.5 } ^ 2 + 2 A S

=> AS = - { 3.5 } ^ 2 / 2

=> S = { -12.25 / 2 A }

Now,

Let us find the acceleration of the body.

The downward Acceleration is g, acceleration due to gravity.

Now,

The required Angle of inclination = 30°

The X component of Acceleration = - g cos 30°

The Y component of Acceleration = - g sin 30° { The required acceleration }

So, Now let us find the value of S

=> S = { -12.25 / -2 g sin 30° }

=> S = { -12.25 / - g } ( as 2 and sin 30° get canlcelled )

=> S is approximately equal to 1.225 metres taking the value of g as 10.

ANSWER :

After the cyclist stops pedaling, he will cover 1.225 Metres up the hill before stopping.

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