Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Banner 9

Q.

A cart is moved horizontally with a constant velocity of 4 m/sec. A ball is thrown from it with a velocity of 4 m/sec and at an angle θ with the horizontal with respect to the cart. Assume the height of the cart is very small, so that the motion of the ball is assumed to be a ground-to-ground projectile. Horizontal range of the ball with respect to the ground is R1 and that with respect to the cart is R2. Then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya

a

R1 will be maximum for θ=60∘

b

R1 will be maximum for θ=90∘

c

R2 will be maximum for θ=60∘

d

R2 will be maximum for θ=45∘

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

Range with respect to ground R=2uxuyg=2(4+4cos⁡θ)(4sin⁡θ)gR=32sin⁡θ(1+cos⁡θ)g=32g(sin⁡θ+sin⁡θcos⁡θ)Rmax when sin⁡θ+sin⁡θcos⁡θ will be max ⇒ ddθ(sin⁡θ+sin⁡θcos⁡θ)=0⇒ cos⁡θ+2cos2⁡θ−1=0⇒ cos⁡θ=12⇒θ=60∘Since the lvelocityl of the ball w.r.t. to the cart is constant. So range w.r.t. to the cart will be max when θ = 45o
Watch 3-min video & get full concept clarity
score_test_img

courses

No courses found

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

  • promsvg

    live classes

  • promsvg

    progress tracking

  • promsvg

    24x7 mentored guidance

  • promsvg

    study plan analysis

download the app

gplay
mentor

Download the App

gplay
whats app icon
personalised 1:1 online tutoring