Exams › JEE Advanced › Physics

A shell is fired from a cannon. At a point when the shell is at half its maximum height H, it moves at 45° to the horizontal. Exactly 2 seconds later, the shell is moving horizontally (i.e., it is at the maximum height). Given g = 10 m/s², find the maximum height H.

1. 20 m
2. 20 sqrt(2) m
3. 40 m
4. 40 sqrt(2) m

Correct answer: 40 m

Solution

At half max height, angle = 45° means vy = vx at that point. Time to reach max height from H/2 is 2 s, so vy_half = g × 2 = 20 m/s. Energy/kinematics from H/2 to H: vy_half² = 2g(H/2), giving H = vy_half²/g = 400/10 = 40 m.

Related JEE Advanced Physics questions

• Rain is falling at an angle α with respect to the vertical at a velocity of 10 m/s. A girl runs in the opposite direction to the rain at a speed of 8 m/s and observes that the rain appears to make an angle β with the vertical. What is the relationship between α and β?
• A vector A is turned by a very small angle Δθ radians (where Δθ is much less than 1) to form a new vector B. What is the magnitude of the difference |B − A|?
• A swimmer moves through water at a speed of v relative to the water. To cross a river of width d, which flows at a speed u (where u < v), the downstream displacement caused by the river's flow is x. Which of the following is accurate?
• A particle is launched from a point with an initial speed u at an angle θ above the horizontal. At a specific point during its motion, its velocity becomes perpendicular to its original direction. What is the time taken to reach this point?
• A particle of mass m is projected form the ground with an initial speed u₀ at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u₀. The angle that the composite system makes with the horizontal immediately after the collision is
• A projectile is launched from level ground with an initial velocity v at an angle θ to the horizontal. The range of the projectile is initially d when the gravitational acceleration is g. If, at the peak of its motion, the projectile enters a zone where the effective gravitational acceleration becomes g' = g/0.81, the new range becomes d'. What is the value of n?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →