When a ball is thrown horizontally, its initial vertical velocity is zero, but it still experiences the acceleration due to gravity (9.8 m/s²) in the downward direction. The horizontal motion of the ball does not affect the time it takes to reach the ground because the vertical and horizontal motions are independent of each other.
To find the time it takes for the ball to reach the ground, we can focus on the vertical motion. We can use the equation:
d=ut+12gt2d = ut + frac{1}{2}gt^2d=ut+21gt2
Where:
- d is the vertical displacement (in this case, -80 m because it is going downward)
- u is the initial vertical velocity (0 m/s)
- g is the acceleration due to gravity (-9.8 m/s²)
- t is the time taken
Substituting the known values into the equation:
−80=0⋅t+12⋅(−9.8)⋅t2-80 = 0 cdot t + frac{1}{2} cdot (-9.8) cdot t^2−80=0⋅t+21⋅(−9.8)⋅t2
Simplifying the equation:
−80=−4.9t2-80 = -4.9t^2−80=−4.9t2
Dividing both sides by -4.9:
16.3265=t216.3265 = t^216.3265=t2
Taking the square root of both sides:
t=16.3265≈4.04 secondst = sqrt{16.3265} approx 4.04 ext{seconds}t=16.3265≈4.04 seconds
Therefore, it takes approximately 4.04 seconds for the ball to reach the ground.