Let h = distance (m) to the water surface.
Initial velocity, u = 0 (because the stone was dropped).
Use the formula
h = ut + (1/2)gt^2
where g = 9.8 m/s^2 (acc. due to graity)
t = time (s)
h = (1/2)*(9.8)*(3^2) = 44.1 m
First
let us imagine the projectile launched at initial velocity V and at angle
θ relative to the horizontal. (ignore wind resistance)
Vertical component y:
The
initial vertical velocity is given as Vsinθ
The moment the projectile reaches the maximum
height of h, the vertical velocity
will be 0, therefore the time t taken to attain this maximum height is:
h = Vsinθ - gt
0 = Vsinθ - gt
t = (Vsinθ)/g
where
g is acceleration due to gravity
Horizontal component x:
The initial horizontal velocity is given as Vcosθ. However unlike
the vertical component, this horizontal velocity remains constant because this is unaffected by gravity. The time to travel the
horizontal distance D is twice the value of t times the horizontal velocity.
D = Vcosθ*[(2Vsinθ)/g]
D = (2V²sinθ cosθ)/g
D = (V²sin2θ)/g
In order for D (horizontal distance) to be
maximum, dD/dθ = 0
That is,
2V^2 cos2θ / g = 0
And since 2V^2/g must not be equal to zero, therefore cos(2θ) = 0
This is true when 2θ = π/2 or θ = π/4
Therefore it is now<span> shown that the maximum horizontal travelled is attained when
the launch angle is π/4 radians, or 45°.</span>
To find or discover by investigation?
Answer:
The ladder is 3.014 m tall.
Explanation:
To solve this problem, we must use the following formula:
v = x/t
where v represents the woman’s velocity, x represents the distance she climbed (the height of the ladder), and t represents the time it took her to move this distance
If we plug in the values we are given for the problem, we get:
v = x/t
2.20 = x/1.37
To solve this equation for x (the height of the ladder), we must multiply both sides by 1.37. If we do this, we get:
x = (2.20 * 1.37)
x = 3.014 m
Therefore, the ladder is 3.014 m tall.
Hope this helps!
Answer:
2 m/s
Explanation:
= Mass of red truck = 1000 kg
= Mass of green truck= 3000 kg
= Initial Velocity of red truck = 6 m/s
= Initial Velocity of green truck
= Velocity with which they move together = 0
For elastic collision
Velocity of the green truck is 2 m/s
