Force and Motion Test. 3

The time of flight is the total time the projectile is in the air. It is twice the time taken to reach the maximum height, which is (v_i sinθ)/g.

Action-reaction pairs act on the two different interacting bodies. Forces can only cancel out if they act on the same body.

The force exerted by the person is vertically upwards to counteract gravity, while the displacement is horizontal. The angle between them is 90°, and since W = Fd cos(90°), the work done is zero.

The normal force (apparent weight) must support the true weight (mg) and also provide the upward acceleration (ma). Thus, N = mg + ma = m(g+a).

Escape velocity is the minimum speed an object needs to break free from a planet's gravitational pull without further propulsion. For Earth, this is about 11.2 km/s.

Using the law of cosines for vector addition, R² = A² + B² + 2ABcosθ. If R=A=B, then A² = A² + A² + 2A²cosθ, which simplifies to cosθ = -1/2. Thus, θ = 120°.

For a variable force, the work done is the integral of F with respect to displacement, which is geometrically represented by the area under the Force-Displacement graph.

Newton's First Law describes an object's tendency to resist changes in its state of motion, which is the definition of inertia.

Using s = v_i*t + ½gt², with v_i = 0, the distance is s = ½(9.8)(2)² = 19.6 m.

Displacement is a vector (start to end point), while distance is a scalar (total path). An object can travel a non-zero distance and return to its starting point, making its displacement zero while distance non zero.

Force is a vector quantity, and as such, it requires both a magnitude (how strong it is) and a direction to be fully described.

This formula relates the initial vertical velocity component to the maximum height reached against gravity, derived from v_f² = v_i² + 2as.

An explosion is caused by internal forces. In the absence of external forces, the total momentum of the system (the rock pieces) is conserved.

The work done by a conservative force (like gravity) between two points depends only on the initial and final positions, not on the path followed between them.

The value of 'g' is slightly greater at the poles than at the equator due to the Earth's shape and rotation. Since Weight = mg, the weight increases.

In a perfectly inelastic collision, the objects stick together after impact, meaning their relative velocity of separation is zero. The coefficient of restitution e is the ratio of relative separation velocity to relative approach velocity, so e=0.

Uniform motion implies constant velocity. Therefore, the velocity does not change over time.

Retardation (deceleration) means the velocity is decreasing. A decreasing velocity is represented by a negative slope on a velocity-time graph.

The change in momentum (impulse) is calculated as Force × time. Δp = 100 N × 10 s = 1000 Ns or 1000 kg m/s.

Relative to the car's frame of reference, the man is not changing his position. Therefore, his speed with respect to the car is zero.