Final answer:
To find the initial horizontal velocity for the clothes to land in the basket, we need to solve for the time it takes to fall vertically and use this to calculate the necessary horizontal velocity.
Step-by-step explanation:
The student's question pertains to projectile motion, which is a concept in physics. The question is asking for the initial horizontal velocity for the clothes that must be given to land in a basket that is 0.400 meters away horizontally and 0.600 meters below the chute opening. To solve this, we need to consider both the horizontal and vertical motions separately, as they are independent of each other in projectile motion.
Firstly, we need to determine the time t it takes for the clothes to fall 0.600 meters vertically. Using the kinematic equation for vertical motion:
s = ut + 0.5at^2
For vertical motion, u (initial vertical velocity) is 0 m/s, a (acceleration due to gravity) is approximately 9.81 m/s^2, and s (vertical displacement) is -0.600 m (downwards).
Substituting the values, we get:
-0.600 = 0 + 0.5 * 9.81 * t^2
By rearranging and solving for t, we find the time it takes to fall 0.600 meters.
Next, we use the horizontal component of the motion to find the horizontal velocity v.
The horizontal displacement x is given as 0.400 meters and the horizontal acceleration is 0 m/s^2 (there is no acceleration horizontally as there is no air resistance).
To find the horizontal velocity:
x = vt
Since we have already found the time t, we simply rearrange the equation to solve for v, which is the horizontal velocity needed for the clothes to reach the basket.