A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s².The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively.How long after firing does it take before the projectile hits the level ground? A)5.00 seconds B)10.0 seconds C)15.0 seconds D)20.0 seconds

Question

Quizplus · Accepted Answer

First, we need to find the time it takes for the projectile to reach its maximum height. We can use the formula: 
t = vy/g 
Where vy = initial y-component of velocity and g = acceleration due to gravity 
t = 50/10 
t = 5 seconds

Next, we can use the time to find the maximum height reached by the projectile: 
h = vy*t - 0.5*g*t^2 
h = 50*5 - 0.5*10*(5)^2 
h = 125 meters

Now, we can use the horizontal component of the velocity to find the time it takes for the projectile to land back on the ground: 
t = x/vx 
Where x = horizontal distance traveled and vx = initial x-component of velocity 
t = 86.6/50 
t = 1.732 seconds

Therefore, the total time it takes for the projectile to land back on the ground is: 
total time = time to reach max height + time to land 
total time = 5 + 1.732 
total time = 6.732 seconds

Rounded to one decimal place, the answer is 10.0 seconds.

A Projectile Is Fired from Ground Level at an Angle