Math Solutions

A train of length 120 m is moving at a speed of 54 km/h. How long will it take to cross a man standing on the platform? How long will it take to cross a platform of length 180 m?

A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Find when and where it hits the ground.

A car takes 10 seconds to overtake a truck and 20 seconds to cross a bridge. 👉 Question: Which is longer — the truck or the bridge?

The Cricket Reaction Puzzle Shoaib Akhtar bowls a delivery at 150 km/h towards Sachin Tendulkar. The distance between them is 20 meters. 👉 Question: How much time does Sachin actually get to react and play the shot?

train with 12 bogies takes 24 seconds to completely pass a pole. At every station, 2 bogies are removed. After stopping at 3 stations, the train again passes a pole at the same speed. 👉 Question: How much time will the train now take to completely pass the pole?

Two trains are moving in opposite directions: Train A: 60 km/h, length 100 m Train B: 40 km/h, length 150 m 👉 Question: Time to completely cross each other?

The sun makes an angle of 30° with the ground. A pole is 10 m tall. 👉 Question: How long is its shadow?

A roller coaster starts from rest at a height of 60 m. It goes down a frictionless track, passes through a loop of radius 10 m, and then climbs another hill.

A lifeguard stands on one bank of a river flowing at 4 m/s. A person is drowning 50 m downstream from a point directly opposite the lifeguard. The lifeguard can run along the bank at 6 m/s and swim in still water at 3 m/s.

A delivery drone is flying horizontally at a constant speed of 20 m/s at a height of 80 m above the ground. There is a horizontal wind blowing in the opposite direction with a speed of 5 m/s (affecting only the package after release). At a certain point, the drone releases a package to deliver it to a person standing on the ground.

A car A is moving at 20 m/s. Another car B starts from rest at the same point and accelerates at 4 m/s².

A car A is moving at 20 m/s. Another car B starts from rest at the same point and accelerates at 4 m/s².

A ball is thrown from the top of a building of height 20 m with an initial velocity of 15 m/s at an angle of 30° above the horizontal.

A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Find when and where it hits the ground.

Two trains are moving in opposite directions on parallel tracks. Train A is 150 meters long and moving at a speed of 60 km/h. Train B is 100 meters long and moving at a speed of 40 km/h. How much total distance must they cover to completely pass through each other? Also, calculate the time taken for them to completely cross each other.

Two trains are moving in opposite directions on parallel tracks. Train A is 150 meters long and moving at a speed of 60 km/h. Train B is 100 meters long and moving at a speed of 40 km/h. How much total distance must they cover to completely pass through each other? Also, calculate the time taken for them to completely cross each other.

Two vectors: A = 5 units at 30° and B = 8 units at 120°. Find and visualize their resultant vector.

If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines.

A small candle, 2.5 cm in size, is placed at 27 cm in front of a concave mirror of a radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?