TS EAMCET · Physics · Motion In Two Dimensions

A projectile is launched with an initial speed of $40 m s^{- 1}$ at an angle $30 °$ above the ground. The projectile lands on a hillside $2.0 s$ later. The net displacement from where the projectile was launched to where it hits the target is (Take $g = 10 m s^{- 2}$ )

A $20 \sqrt{3} m$
B $30 \sqrt{2} m$
C $40 m$
D $20 \sqrt{13} m$

Verified Solution

Answer & Solution

Correct Answer

(D) $20 \sqrt{13} m$

Step-by-step Solution

Detailed explanation

Horizontal displacement covered, x=40cos30°×2=403 m Vertical displacement covered, y=40sin30°×2+12-10×22=40-20=20 m Hence, required displacement will be, x2+y2=2013 m

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A projectile is launched with an initial speed of 40 m s-1 at an angle 30° above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile was launched to where it hits the target is (Take g=10 m s-2)

Step-by-step Solution

A projectile is launched with an initial speed of $40 m s^{- 1}$ at an angle $30 °$ above the ground. The projectile lands on a hillside $2.0 s$ later. The net displacement from where the projectile was launched to where it hits the target is (Take $g = 10 m s^{- 2}$ )