Question

a block is launched up a frictionless ramp that makes an angle of 35 to the horizontal. if the block’s initial speed is 2.2 m/s, how far up the ramp does the block slide?

Answer 1

The block is going upwards,against gravity so the acceleration due to gravity is negative

Answer 2

The block's initial kinetic energy is converted into gravitational potential energy as it moves up the ramp. Using the conservation of energy and the relationship between height and distance along the ramp, the distance the block slides can be calculated from its initial speed, gravity, and the ramp's incline angle.

Step-by-step explanation:

To find out how far up the ramp the block slides, we can use the principles of conservation of energy because friction is negligible and the only forces doing work are conservative. The initial kinetic energy of the block is converted into gravitational potential energy at the peak of its motion up the ramp. The initial kinetic energy (KEi) can be calculated using the formula KEi = 1/2 * m * v2, where m is the mass of the block and v is its initial velocity.

Gravitational potential energy (PE) at the peak is given by PE = m * g * h, where g is the acceleration due to gravity and h is the height reached. Since the ramp makes an angle with the horizontal, the height can be related to the distance up the ramp, d, by the trigonometric relationship h = d * sin(θ), where θ is the angle of incline.

Setting the initial kinetic energy equal to the gravitational potential energy at the peak and solving for d, we get:
1/2 * m * v2 = m * g * d * sin(θ)
Hence, d = (v2) / (2 * g * sin(θ)). Plugging in the values, with v = 2.2 m/s, g = 9.81 m/s2, and θ = 35°, we can calculate the distance.