a vending machine ate another students dollar. the student had enough. he dropped the vending machine off a 20 m cliff. at the same time his buddy at the bottom of the cliff throws a grenade straight up towards the vending machine. the grenade strikes the vending machine after .3 seconds. how far up the cliff does the grenade impact the vending machine?
See previous post for solution.
To determine how far up the cliff the grenade impacts the vending machine, we need to calculate the vertical distance it travels due to the initial throw and the time it takes for the grenade to reach the vending machine.
1. First, let's calculate the vertical distance travelled due to the initial throw.
Gravity acts on the grenade, causing it to accelerate downwards. The equation to calculate the distance traveled is given by:
d = 0.5 * g * t^2
where d is the vertical distance, g is acceleration due to gravity (approximately 9.8 m/s^2), and t is the time in seconds.
Since the initial throw doesn't involve a projectile motion, we can assume that the grenade was thrown directly upwards with an initial velocity of 0 m/s. Therefore, the time it takes for the grenade to reach its peak and start descending is equal to the time it takes to reach halfway up the trajectory. So, the time t = 0.3 seconds.
Using the given values and substituting them into the equation, we get:
d = 0.5 * 9.8 * (0.3)^2
d = 0.5 * 9.8 * 0.09
d ≈ 0.441 meters
2. The vending machine was dropped off a 20 m cliff. Therefore, to find the impact point, we need to subtract the distance traveled due to the initial throw from the height of the cliff.
Impact point = 20 - 0.441
Impact point ≈ 19.559 meters
So, the grenade impacts the vending machine at approximately 19.559 meters up the cliff.