A hemispherical dome has a diameter of 100m. A search light has placed at a point A located at the circumference at the base. At the middle of the dome at B , a balloon was released vertically at a velocity of 4m/sec. How fast will the shadow of the balloon move along the roof if it traveled 25m high?
Answers
Mark me as brainliest I will also mark you
The shadow will move with a speed of 8 m/s.
Consider a hemispherical dome with a base diameter of 100 metres, as mentioned. Point A is located at one end of the diameter on the circumference of the hemisphere. Point B is at the centre of the diameter at a distance of 50 meters from point A.
From point B, a balloon is released at the velocity of 4 m/s. The balloon rises to a height of 25 meters which has to be the height of the hemisphere.
Hence, the shadow on the ground has to move from point A to point B thus covering a distance of 50 meters.
Let us calculate time taken by the balloon to rise 25 meters.
Time = Distance / Velocity
= 25 / 4
= 6.25 sec
The same time is required for the shadow to move along the ground from point B to point A.
Thus, as velocity = distance / time
Velocity of Shadow = Distance travelled / time
= 50 / 6.25
= 8 m/s