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geniusboy [140]
3 years ago
11

On a cold day, hailstones fall with a velocity of 2i − 6k m s−1 . If a cyclist travels through the hail at 10i m s−1 , what is t

he velocity of the hail relative to the cyclist? At what angle are the hailstones falling relative to the cyclist?
Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer:

The velocity of the hail relative to the cyclist is V_{hc}=-8\hat{i}-6\hat{k}

The angle at which hailstones falling relative to the cyclist is \theta = 36.86^\circ

Step-by-step explanation:

Given : On a cold day, hailstones fall with a velocity of 2\hat{i}-6\hat{k}\text{ m/s} . If a cyclist travels through the hail at 10\hat{i} \text{ m/s}.

To find : What is the velocity of the hail relative to the cyclist and At what angle are the hailstones falling relative to the cyclist?

Solution :

The velocity of the hailstone falls is V_h=2\hat{i}-6\hat{k}\text{ m/s}

The velocity of the cyclist travels through the hail is V_c=10\hat{i} \text{ m/s}

The velocity of the hail relative to the cyclist is given by,

V_{hc}=V_h-V_c

Substitute the value in the formula,

V_{hc}=2\hat{i}-6\hat{k}-10\hat{i}

V_{hc}=-8\hat{i}-6\hat{k}

So, The velocity of the hail relative to the cyclist is V_{hc}=-8\hat{i}-6\hat{k}

Now, The angle of hails falling relative to the cyclist is given by

\theta = \tan^{-1}(\frac{-6}{-8})

\theta = \tan^{-1}(\frac{3}{4})

\theta = 36.86^\circ

So, The angle at which hailstones falling relative to the cyclist is  \theta = 36.86^\circ

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