The speed of the boy is 62.832 m/s and the velocity is 56.56854 m/s.
Step-by-step explanation:
Given:
A boy is travelling along a circular path of radius 400m.
He covers 1/4th of the circular path in 10 seconds.
To Find: Speed and Velocity of the boy.
Calculation:
We know that,
Speed = Distance Travelled / Time
Velocity = Displacement / Time
Distance travelled is the 1/4th of the circumference of the circular path.
Circumference of a circle = ( 2π x radius ) unit
= 2π x 400 m
= 2513.2741 m [ rounded to decimal place ]
Distance covered = 2513.2741 / 4 m
= 628.32 m [ rounded to 2 decimal place ]
Total angle around the center of the circle = 360º
1/4th of the total angle = 360º/4 = 90º
Therefore the starting point, ending point and the center of the circular path forms a Right Angled Triangle, where the hypotenuse of the triangle is the displacement of the boy.
Length between starting point and center = Length between ending point and center = radius of the circular path
Therefore, Displacement = √ (400² + 400²) m
= 565.6854 m [ Rounded to 4 Decimal Place ]
Speed = 628.32 / 10 = 62.832 m/s
Velocity = 565.6854 / 10 = 56.56854 m/s
Hence, The speed of the boy is 62.832 m/s and the velocity is 56.56854 m/s. ( ans. )
Answers & Comments
Answer:
The speed of the boy is 62.832 m/s and the velocity is 56.56854 m/s.
Step-by-step explanation:
Given:
To Find:
Speed and Velocity of the boy.
Calculation:
We know that,
Speed = Distance Travelled / Time
Velocity = Displacement / Time
Distance travelled is the 1/4th of the circumference of the circular path.
Circumference of a circle = ( 2π x radius ) unit
= 2π x 400 m
= 2513.2741 m [ rounded to decimal place ]
Distance covered = 2513.2741 / 4 m
= 628.32 m [ rounded to 2 decimal place ]
Total angle around the center of the circle = 360º
1/4th of the total angle = 360º/4 = 90º
Therefore the starting point, ending point and the center of the circular path forms a Right Angled Triangle, where the hypotenuse of the triangle is the displacement of the boy.
Length between starting point and center = Length between ending point and center = radius of the circular path
Therefore, Displacement = √ (400² + 400²) m
= 565.6854 m [ Rounded to 4 Decimal Place ]
Speed = 628.32 / 10 = 62.832 m/s
Velocity = 565.6854 / 10 = 56.56854 m/s
Hence, The speed of the boy is 62.832 m/s and the velocity is 56.56854 m/s. ( ans. )