A projectile is launched from ground level at an angle of 45 degrees above the horizontal with a speed of 40m/s. It is aimed straight towards a high wall that is a horizontal distance of 120m away from the launch point.
a) How much time will the projectile spend in the air before it hits the wall?
b) At what hight above the ground level will the projectile hit the wall?
assume it hits wall.
distance=vh*time
120=40*cos45*time
time=30/cos45
hf=hi+vvi*timeinair-4.9 t^2
put in time t, and calculate hf.
vvi=40sin45
is hi equal to zero?
Also time = 3/cos45 not 30
To solve this problem, we can break it down into two components: the horizontal and vertical motion of the projectile.
a) The horizontal motion of the projectile is independent of the vertical motion, meaning that the time it takes to hit the wall is the same as the time it would take to cover the horizontal distance of 120m. We can calculate this time using the formula:
time = distance / speed
Given that the distance is 120m and the speed is 40m/s, we have:
time = 120m / 40m/s = 3s
Therefore, the projectile will spend 3 seconds in the air before hitting the wall.
b) Now, let's determine the height above the ground level where the projectile will hit the wall. To do this, we need to calculate the vertical distance traveled by the projectile.
We can use the kinematic equation for vertical motion:
displacement (Δy) = velocity (v) * time (t) + (1/2) * acceleration (a) * time^2
In this case, the initial vertical velocity (viy) is given by:
viy = v * sinθ
where v is the initial speed and θ is the launch angle. Given that v = 40m/s and θ = 45 degrees, we find:
viy = 40m/s * sin(45°) = 28.28m/s
Since we know the time (t) is 3 seconds (from part a), and the acceleration (a) is -9.8m/s^2 (assuming downward motion), we can substitute these values into the equation:
Δy = 28.28m/s * 3s + (1/2) * (-9.8m/s^2) * (3s)^2
Simplifying the equation:
Δy = 84.84m + (1/2) * (-9.8m/s^2) * 9s^2
Δy = 84.84m - 44.1m
Δy = 40.74m
Therefore, the projectile will hit the wall at a height of approximately 40.74 meters above the ground level.