Question

An object is thrown horizontally with an initial velocity of 10m/s. If it takes 5 seconds to hit the ground, how far did it travel horizontally?

Answer 1

When an object is thrown horizontally, its initial vertical velocity is zero, and it only experiences the effect of gravity in the vertical direction. The horizontal velocity remains constant throughout the motion.

Given that the object takes 5 seconds to hit the ground, we can focus on the vertical motion to determine the time of flight and then calculate the horizontal distance traveled.

In the vertical direction, we can use the equation of motion:

$y=y_0+v_{0y}t+\frac{1}{2}a{t}^2$

where:

• $y$ is the vertical displacement (in this case, the object's initial height is zero and the final height is the ground level, so $y=0-0=0$),
• $y_0$ is the initial vertical position (zero in this case),
• $v_{0y}$ is the initial vertical velocity (also zero in this case),
• $a$ is the acceleration due to gravity (-9.8 m/s², assuming downward direction), and
• $t$ is the time of flight (5 seconds in this case).

Plugging in the values, the equation becomes:

0=0+0+12(−9.8)(52)0 = 0 + 0 + frac{1}{2}(-9.8)(5^2)0=0+0+2<span class="frac-line" style="border-bo