Final answer:
To find the maximum height the cork reaches and its velocity after 1 second, we calculate its vertical velocity, apply kinematic equations for projectile motion, and consider gravity's effect on the vertical component while ignoring air resistance.
Step-by-step explanation:
A student asked how high a cork would travel when it shoots out of a champagne bottle at an initial velocity of 24.0 m/s at an angle of 35.0° above the horizontal, and what its velocity would be after 1 second.
To answer the question:
- We need to calculate the vertical component of the initial velocity using the formula: vertical velocity (Vy) = V * sin(θ), where V is the initial velocity and θ is the angle of projection.
- With the vertical velocity, we can determine the maximum height using the formula for vertical motion under gravity: h = Vy^2 / (2 * g), where g is the acceleration due to gravity.
- After 1 second, to find the velocity, we must consider both the horizontal and vertical components affected by gravity. The horizontal component remains constant while the vertical component changes due to gravity: final vertical velocity (Vyf) = Vy - g * t.
The detailed calculations yield the specific values for the maximum height (h) and the velocity of the cork after 1 second.