Motion In A Plane

If the boy A catches boy B in time t,
then vt₂ = (v₁t)² + a²
⇒
⇒

Therefore , the correct option is (D) : .

Calculation of Velocity (V) using given parameters

We are given the following equation:

Now, substitute , where , into the equation:

This simplifies to:

Next, the acceleration is given by:

Substitute the value of into the equation:

Square both sides to eliminate the square root:

Simplify the equation:

Now, isolate :

Now take the square root of both sides:

Finally, solve for using the equation:

After simplifying:

The velocity is:

To determine the maximum height attained by the bullet, we use the vertical component of the initial velocity and the kinematic equations. Given:

• Initial velocity, v₀ = 280 m/s
• Angle above horizontal, θ = 30°
• Acceleration due to gravity, g = 9.8 m/s²
• sin 30° = 0.5

The vertical component of the initial velocity, v_0y, is given by:

v_0y = v₀ × sin θ = 280 m/s × 0.5 = 140 m/s

Using the kinematic equation for maximum height (H):

v² = v_0y² − 2gH

At maximum height, the vertical velocity (v) = 0:

0 = (140 m/s)² − 2 × 9.8 m/s² × H

Solving for H:

2 × 9.8 m/s² × H = 19600 m²/s²

H = 19600 m²/s² / 19.6 m/s² = 1000 m

Thus, the maximum height attained by the bullet is 1000 m.

The correct option is (D): along the tangent to its position

Angular acceleration is due to Torque. Suppose there is a plane of a circle, and the body is moving along with the circumference of a circle. 

Torque, τ = I x α

I = moment of inertia 

and the angular direction is towards the direction of the Torque.

and, the direction of the Torque is, τ = r × F

Where r is the radius and F is the perpendicular tangent. 

and the direction of torque is perpendicular to r and perpendicular to F. r and F lie perpendicular to the circle. If the two vectors lie in a circle of a plane, then the cross product of two vectors lies on the perpendicular. And, if the torque lies on the perpendicular of the plane, then the angular acceleration will also lie on the perpendicular of the plane. Hence the correct answer is option D, long the tangent to its position.