Q. 293.8( 4 Votes )

A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m/s over the hill. The canon is located at a distance of 800m from the foot of hill and can be moved on the ground at a speed of 2 m/s; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? Take g =10 m/s2.

Answer :

Given:


Height of the hill = h = 500m


Speed of projection of packets = u = 125m/s


Distance of canon = 800m


Speed of canon = v = 2m/s



For time to be minimum, the packet should just pass the top of the hill and so the vertical component of velocity must be minimum.


So,


Now let’s calculate the horizontal component of velocity.



Now, for time to reach the top of the hill,



Hence, 20 seconds is the time of flight.


Now, let’s find the horizontal distance between the canon and top of the hill.


R = uxt = 75m/s×10s =750m


Distance travelled by canon = 800m – 750m = 50m


Time taken by the canon =



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Motion in a Plane - 02Motion in a Plane - 02Motion in a Plane - 0264 mins
Motion in a Plane - 04Motion in a Plane - 04Motion in a Plane - 0460 mins
Motion in a Plane - 01Motion in a Plane - 01Motion in a Plane - 0157 mins
Motion in a Plane - 03Motion in a Plane - 03Motion in a Plane - 0355 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 01Motion in a Straight Line - 01Motion in a Straight Line - 0152 mins
Motion in a Straight Line - 02Motion in a Straight Line - 02Motion in a Straight Line - 0261 mins
Motion in a Straight Line - 04Motion in a Straight Line - 04Motion in a Straight Line - 0459 mins
Motion in a Straight Line - 10Motion in a Straight Line - 10Motion in a Straight Line - 1063 mins
Motion in a Straight Line - 06Motion in a Straight Line - 06Motion in a Straight Line - 0665 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses