Question

13 maybe better not, then. luckily, you notice a ladder. out of curiosity, before descending into the hole, you throw another bat skull up towards the ceiling. you throw it up, counting the seconds as it goes up and comes back down. you catch it after 8 seconds. how fast must you have thrown it?

Answer 1

To find the initial velocity of an object thrown straight up and caught after 8 seconds, we use the equation for uniformly accelerated motion with gravity's acceleration. The object takes 4 seconds to reach the peak, and the initial velocity is found to be 39.24 m/s.

Step-by-step explanation:

Calculating the Initial Velocity of the Thrown Object

To calculate the initial velocity of an object thrown straight up into the air and caught after 8 seconds, we can use the equations of motion for uniformly accelerated motion. The acceleration due to gravity, which is approximately 9.81 m/s2, will cause the object to decelerate on its way up, stop momentarily at the peak of its trajectory, and then accelerate back downwards.

The total time of 8 seconds includes both the ascent and the descent of the object. Therefore, the time it takes to reach the peak is half of 8 seconds, which is 4 seconds.

Using the equation v = u + at, where v is the final velocity (0 m/s at the peak), u is the initial velocity which we are trying to find, a is the acceleration due to gravity (-9.81 m/s2 when considering upward movement as positive and downward as negative), and t is the time, we can rearrange the equation to solve for u:

u = v - at

Plugging in the values, we get:

u = 0 - (-9.81 m/s2)(4 s)

Therefore, the initial velocity u is 39.24 m/s.

This is the speed at which the object must have been thrown upward.