During a basketball game, a player flies above the basket and drops the ball in from a height of 10 meters. If the ball takes 4.4 seconds to fall, find the acceleration due to gravity.
Well, it seems like that basketball player really took flying lessons! Now, to calculate the acceleration due to gravity, we can use the equation of motion for free fall. The vertical displacement can be given by the equation:
𝑑 = 𝑢𝑡 + 0.5𝑎𝑡²
Where:
𝑑 = vertical displacement (10 meters)
𝑢 = initial velocity (0, because the ball was simply dropped)
𝑎 = acceleration due to gravity
𝑡 = time taken (4.4 seconds)
By substituting the values:
10 = (0)(4.4) + 0.5𝑎(4.4)²
Simplifying:
10 = 0 + 0.5𝑎(19.36)
Now, let's find the acceleration due to gravity:
0.5𝑎(19.36) = 10
Dividing both sides by 19.36:
𝑎 = 10 / 19.36
Grabbing my trusty calculator...
𝑎 ≈ 0.516 meters per second squared
So, my friend, the acceleration due to gravity in this case is approximately 0.516 meters per second squared. Just remember, next time you drop something, make sure to shout "Kobe!" for extra accuracy!
To find the acceleration due to gravity, we can use the formula for the freefall motion of an object:
d = v₀t + 1/2gt²
where:
d = distance (in this case, the height of 10 meters)
v₀ = initial velocity (0 m/s as the ball is dropped)
t = time taken (4.4 seconds)
g = acceleration due to gravity (unknown)
Plugging in these values, we get:
10 = 0(4.4) + 1/2g(4.4)²
Simplifying this equation:
10 = 0 + 1/2g(19.36)
10 = 9.68g
g = 10/9.68
Therefore, the acceleration due to gravity is approximately 1.03 m/s².
To find the acceleration due to gravity, we can use the equations of motion.
First, let's denote the initial height of the ball as h0 = 10 meters and the time it takes to fall as t = 4.4 seconds. We know that the acceleration due to gravity acts in the downward direction and its value is constant, denoted by g.
The equation of motion for vertical motion can be written as:
h = h0 + v0*t + (1/2)*g*t^2
In this case, since the ball is dropped from rest and there is no initial vertical velocity (v0 = 0), the equation simplifies to:
h = h0 + (1/2)*g*t^2
Plugging in the given values, we have:
10 = 0 + (1/2)*g*(4.4)^2
To solve for g, we can rearrange and solve the equation:
g = (2*(10))/(4.4^2)
Calculating this, we find:
g ≈ 9.8 m/s^2
Therefore, the acceleration due to gravity is approximately 9.8 m/s^2.