Question

An artificial satellite is moving in a circular orbit of radius42250 km. Calculate its speed if it takes 24 hours to revolve once around the earth

Answer 1

Answer :-

v = 3071 m/s

Given :-

Radius = 42,250 km

t = 24 h

To find :-

The speed of the satellite.

Solution:-

We have r = 42,250 Km

The circumference of circle is given by :-

$\huge \boxed{C= 2\pi r}$

put the given value ,

→$C = 2 \times \dfrac{314}{100}\times 42,250$

→$C = \dfrac{628}{100}\times 42,250$

→$C = 628 \times 422.5$

→$C = 265,330 km$

Now,The distance travelled by satellite is equal to the length of circumference.

S = 265,330 km

= 265,330,000 m

t = 24 h

= 24 × 3600

= 86,400 s

Now,

Speed of the satellite will be:-

→$v = \dfrac{s}{t}$

→$v = \dfrac{265,330,000}{86,400}$

→$v = 3071 m/s$

hence,

The speed of satellite will be 3071 m/s.

Answer 2

Hi there!

The speed of an object moving in a circular orbit (or path) is given by the formula:

$v = \frac{2\pi \: r}{t}$

Speed, v = ? ( We have to calculate )

Pi, π = 22/7 (It is constant)

Radius, r = 42250 km

Time, t = 24 hours

Now, putting these values in the above formula, we get

$v = \frac{2 \times 22 \times 42250}{7 \times 24} \\ \\ v = 11065.4 \: km \: {h}^{ - 1}$

We can convert this speed from kilometres per hour to kilometres per second by diving it by the number of seconds in 1 hour (which is 60× 60 s).

Thus,

$v \: = \frac{11065.4}{60 \times6 0} \\ \\ v = 3.07km{s}^{ - 1}$

Hence 3.07 kms-1 is the speed if it takes 24 hours to revolve once around the earth.

Thankyou :)