Final answer:
i) To find the time it takes for the stone to hit the ground, we can consider the vertical motion of the stone. Assuming no air resistance, the stone will follow a parabolic path. ii) The horizontal distance from the base of the building can be found by considering the horizontal motion of the stone. iii) The total maximum height reached by the stone can be calculated using the formula for vertical displacement. iv) The speed of the stone just before it strikes the ground can be calculated using the formula for final velocity in projectile motion.
Step-by-step explanation:
i) To find the time it takes for the stone to hit the ground, we can consider the vertical motion of the stone. Assuming no air resistance, the stone will follow a parabolic path. We can use the equation for vertical displacement in projectile motion:
Δy = vy0t + (1/2)gt2
Since the stone is thrown upwards, the initial vertical velocity (vy0) is given by:
vy0 = V0sin(θ)
Using the given values of V0 = 20.0 m/s and θ = 30.0°, we can calculate vy0 = 20.0 * sin(30.0°).
The vertical displacement (Δy) is equal to the negative of the height of the building (-45.0 m). We can substitute these values into the equation and solve for t:
-45.0 = (20.0 * sin(30.0°))t + (1/2)(9.8)t2
Simplifying and solving the quadratic equation will give us the time it takes for the stone to hit the ground.
ii) To find the horizontal distance from the base of the building, we can consider the horizontal motion of the stone. Assuming no air resistance, the horizontal velocity remains constant throughout the motion. The horizontal distance (x) can be calculated using the equation:
x = V0cos(θ)t
Using the given values of V0 = 20.0 m/s and θ = 30.0°, we can calculate x.
iii) The total maximum height reached by the stone can be calculated using the formula for vertical displacement:
Δy = vy0t + (1/2)gt2
Since the stone is thrown upwards, the initial vertical velocity (vy0) is given by:
vy0 = V0sin(θ)
Using the given values of V0 = 20.0 m/s and θ = 30.0°, we can calculate vy0 = 20.0 * sin(30.0°).
The time taken for the stone to reach the maximum height will be half of the total time it takes for the stone to hit the ground. We can substitute these values into the equation and solve for the maximum height.
iv) The speed of the stone just before it strikes the ground can be calculated using the formula for final velocity in projectile motion:
v = √(vx2 + vy2)
Since there is no horizontal acceleration, the horizontal velocity (vx) remains constant throughout the motion. The horizontal velocity is given by:
vx = V0cos(θ)
Using the given values of V0 = 20.0 m/s and θ = 30.0°, we can calculate vx = 20.0 * cos(30.0°).
For the vertical velocity (vy), we can use the equation:
vy = vy0 + gt
Using the calculated value of vy0 and the time it takes for the stone to hit the ground, we can calculate vy.
Substituting the calculated values of vx and vy into the equation for final velocity will give us the speed of the stone just before it strikes the ground.