A man is running up hill with a velocity (2 hat i +3 hat j ) m / s w.r.t. ground. He feels that the rain drops are falling vertically with velocity 4 m / s. If he runs down hill with same speed, find vrm.

Question

A man is running up hill with a velocity (2 hat i +3 hat j ) m / s w.r.t. ground. He feels that the rain drops are falling vertically with velocity 4 m / s. If he runs down hill with same speed, find vrm. (A) 2 √2 m / s (B) 2 √3 m / s (C) 2 √5 m / s (D) 2 √10 m / s

Tardigrade Admin · Accepted Answer

vecv m =2 hat i +3 hat j m / s vec v m =-4 hat j m / s vec v r m = vec v r - vec v m -4 hat j = vec v r -(2 hat i +3 hat j ) vec v r =2 i - hat j Now for downward motion. vecv rm = vec v r - vec v m =2 hat i - hat j +(2 hat i +3 hat j )=2 hat i - hat j +2 hat i +3 hat j vec v rm =4 hat i +2 hat j ⇒ | vec v rm |=√20=2 √5 m / s

Q. A man is running up hill with a velocity $(2 \hat{i} + 3 \hat{j}) m / s$ w.r.t. ground. $He$ feels that the rain drops are falling vertically with velocity $4 m / s$ . If he runs down hill with same speed, find $v_{r m}$ .

$22 m / s$

$23 m / s$

$25 m / s$

$210 m / s$

Q. A man is running up hill with a velocity (2i^+3j^​)m/s w.r.t. ground. He feels that the rain drops are falling vertically with velocity 4m/s. If he runs down hill with same speed, find vrm​.

22​m/s

23​m/s

25​m/s

210​m/s

vm​=2i^+3j^​m/s vm​=−4j^​m/s vrm​=vr​−vm​ −4j^​=vr​−(2i^+3j^​) vr​=2i−j^​ Now for downward motion. vrm​=vr​−vm​=2i^−j^​+(2i^+3j^​)=2i^−j^​+2i^+3j^​ vrm​=4i^+2j^​ ⇒∣vrm​∣=20​=25​m/s

Q. A man is running up hill with a velocity $(2 \hat{i} + 3 \hat{j}) m / s$ w.r.t. ground. $He$ feels that the rain drops are falling vertically with velocity $4 m / s$ . If he runs down hill with same speed, find $v_{r m}$ .

$22 m / s$

$23 m / s$

$25 m / s$

$210 m / s$