please help! physics projectile question

Question

The Iron Chef Hiroyuki Sakai is rapidly chopping the stems off a batch of green beans and flicking them off the edge of the counter into the trash. If the counter is a height h=1.26 m above the trash, which is sitting a distance d=0.79 m past the edge of the counter, then how fast must he flick the stems? Make sure you do the following in your answer:
DO NOT include units. We'll deal with that in the next question.
Give precision to hundreths (#.##).
Make your answer correct to within 0.02

Answer 1

Hi Lauren.

 

This question is asking you find the horizontal velocity component of the projectile. If you know how long the stems will be in the air, you can use the known horizontal distance required to reach the trash can to calculate your required velocity.

 

You're told the fall to the trash can is 1.26 meters. Since the chef is not throwing the stems down into it, you can assume the initial vertical velocity of the stem is 0 m/s. Hence, only gravity will be acting on it. This will greatly simplify your equation. Let's figure out how long it will take the stem to fall from the counter to the trash can.

 

h = 1/2*g*t^2

 

1.26m = 1/2*9.8*t^2

 

t^2 = 0.25714

 

t = 0.51 seconds

 

Cool, so you know the travel time for the stem will be 0.51 seconds before it lands in the trash can. You also know it has to travel 0.79 meters. If the stem wants to cover a distance of 0.79 meters in just 0.51 seconds, it must be traveling at a velocity of:

 

0.79 m / 0.51 sec = 1.55 m/sec

 

The Iron Chef has to send the stems at a rate of 1.55 m/sec

 

Hope this helps.