1. A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?
Since the motion is uniform, we can say that at time t+15 seconds, the plane is above the point is
diametrically opposite to the point P from where the angle is same.
Now since the time taken to cover the full circ
le is 3 minutes (180
seconds), the time taken by the plane
to reach the diametrically opposite point will be 90 seconds.
So the time after which the plane reaches the point P will be = t+ 15 + 90 seconds = (t + 105 )seconds
2. A race has three parts. The speed and time required to complete the individual parts for a runner is displayed on the following chart: Part I Part II Part III Speed (kmph) 9 8 7.5 Time (minutes) 50 80 100 What is the average speed of this runner?
4. Raghu goes to college at a speed of 4 kmph and returns at a speed of 3 kmph. If he takes 5.95 hrs in all, then what is the distance between his home and the college?
5. A boy starts from his house and walks at a speed of 5 km/hr and reaches his school 3 minutes late. Next day he starts at the same time and increases hisspeed by 4 km/hr and reaches 3 minutes early. What is the distance (in km) between the school and his house?
8. To travel 612 km, an Express train takes 9 hours more than Rajdhani. If the speed of the Express train is doubled, it takes 3 hours less than Rajdhani. The speed (in km/hr) of Rajdhani is
9. Two cyclists P and Q cycle at 20 km/hr and 16 km/hr towards each other respectively. What was the distance (in kms) between them when they started if they met after 40 minutes?