Respuesta :
Answer:
The second ball hits the ground at the same time as ball 1, after 5 seconds
Explanation:
Step 1: Data given
We have 2 balls at the same height (h)
The 2 balls are released at the same time (t=0)
Ball 1 hits the ground after 5 seconds ( t1= 5s)
Step 2
Since ball 1 immediately falls down, this means it only has downward velocity
t1 is the time needed for ball 1 to hit the ground
The formula for time is d/v1
⇒where d = distance (in this case vertical)
⇒where v1 = (downwards) velocity of ball 1
We can also say that the more time, the higher the (downwards) velocity. This is because when the ball falls, it's subject to gravity:
v = gt
But ball 1 has no initial velocity. The velocity is gained due to the gravity only after falling down.
When we write this in formulas we'll have:
dy = vyt + [tex]\frac{1}{2}[/tex]gt²
⇒where Vy is the initial vertical velocity of ball 1 = 0
⇒where dy = the vertical distance of ball 1
⇒t = the time
⇒ g= the gravitational constant = 9.81 m/s²
dy = [tex]\frac{1}{2}[/tex]gt² = h = the distance the ball has fallen
From this formula we can calculate the time t needed to hit the ground
t = [tex]\sqrt{\frac{2h}{g} }[/tex]
Ball 2 initially moves horizontally, but is thrown from the same height
this means ball 2 will have the same downwards velocity (=v1)
But also a horizontally velocity =( v2) causing the initial horizontal move.
Ball 2 has an initial horizontal velocity but no initial vertical velocity. only after it's moving horizontally it will gain vertical velocity, this also due to gravity.
When we write this in formulas we'll have:
dy = vyt + [tex]\frac{1}{2}[/tex]gt²
⇒where Vy is the initial vertical velocity of ball 2 = 0
⇒where dy = the vertical distance of ball 1
⇒t = the time
⇒ g= the gravitational constant = 9.81 m/s²
h = [tex]\frac{1}{2}[/tex]gt²
From this formula we can calculate the time t needed to hit the ground
t = [tex]\sqrt{\frac{2h}{g} }[/tex]
We can conclude that ball 1 and ball 2 will come down at the same time ( after 5 seconds). The only difference is that ball 2 starts with a initial horizontal velocity, due to this velocity ball 2 will move horizontally. But it gains vertical velocity (just like ball 1) what makes that both the bodies hit the ground at the same time ( after 5 seconds), but a different place.
Read also: https://brainly.com/question/19114958
