Question

A hill is $500m$ high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of $125m/s$ over the hill. The canon is located at a distance of $800m$ from the foot of a hill and can be moved on the ground at a speed of $2m/s$; 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 $g=10m/s^2$.

• A. $45s$
• B. $60s$
• C. $30s$
• D. None of these

Answer 1

The correct option is A $45s$

Speed of particle$=125m.s$

Height of hill$=500m$

distance between canon and hill $d=800m$

Vertical component should be minimum so that it crosses the hill in shortest time

$u_y\ge (2\times 10\times 500{)}^{1/2}\ge 100m/s$

$u^2=u_y^2+u_x^2,u_x^2=(u^2-u_y^2{)}^{1/2}=75m/s$

$t=\sqrt{\frac{2h}{g}}=10s$

Horizental distance covered in $10s$

=u_x\times t=750m$

Time taken by canon$\frac{800-750}{2}=255s$

Time taken by the particle to reach the ground$=25+2\times 10=45s$