Four rocks are thrown horizontally from a building, with varying speeds and from various floors. Rock 1 lands a distance r away from the building, rock 2 lands 2r away from the building, rock 3 lands at distance 3r, and rock 4 at 4r. Ignore air resistance.
Drag the rocks into place to select the rock that was thrown with the height and speed shown. If there was no rock thrown with a certain combination of values, drag "no rock" into that slot. You will use the "no rock" answer more than once.
I kill babies
To determine which rock was thrown with the given height and speed, we need to consider the equation of motion for projectiles. The equation is:
d = v₀t + (1/2)gt²
where:
d is the horizontal distance traveled by the projectile,
v₀ is the initial horizontal velocity of the projectile,
t is the time of flight of the projectile, and
g is the acceleration due to gravity (approximately 9.8 m/s²).
Since we are given the distances the rocks landed (r, 2r, 3r, 4r), we can substitute those values into the equation to find the corresponding values of t.
1. Rock 1 lands at a distance r:
Substitute d = r into the equation:
r = v₀t + (1/2)gt²
Solving for t:
t = (2r / g)^(1/2)
2. Rock 2 lands at a distance 2r:
Substitute d = 2r into the equation:
2r = v₀t + (1/2)gt²
Solving for t:
t = (4r / g)^(1/2)
3. Rock 3 lands at a distance 3r:
Substitute d = 3r into the equation:
3r = v₀t + (1/2)gt²
Solving for t:
t = (6r / g)^(1/2)
4. Rock 4 lands at a distance 4r:
Substitute d = 4r into the equation:
4r = v₀t + (1/2)gt²
Solving for t:
t = (8r / g)^(1/2)
Now, compare the values of t for each rock with the given height and speed combinations. Drag the corresponding rocks into the slots:
- If the height and speed values match a rock's values, drag that rock into the slot.
- If the height and speed values do not match any rock's values, drag "no rock" into the slot.
Remember to use the equation and the distances for each rock to calculate the corresponding values of t.