A bird sitting 16 feet above the ground in an apple tree dislodges an apple. After how many seconds does the apple land on the ground? (Assume no branches interfere with it's fall.)
Use vertical motion model to solve this problem.
h=-16t^2+vt+s
0=-16t^2+(0)t+16. Substitute 0 for h and v, sub 16 for s.
0=-16(t^2-1)
0=-16(t-1)(t+1)
t-1=0. Or. t+1=0
+1 +1 -1 -1
--------- ---------
t=1 t=-1 We can't have negative time so the apple lands on the ground after 1 second.
Hope this helps :)
mmmhhh,
distance that an object falls on earth is governed my
d = 16t^2 , where t is seconds and d is in feet
so 16t^2 = 16
t^2 = 1
t = √1 = 1
To solve this problem using the vertical motion model, we can make use of the equations of motion, specifically the equation for free fall.
The equation for the distance fallen by an object in free fall is:
d = v0 * t + (1/2) * g * t^2
Where:
- d is the distance fallen
- v0 is the initial velocity (in this case, 0, since the apple is at rest when it falls)
- t is the time elapsed
- g is the acceleration due to gravity, which is approximately 32.2 feet per second squared
In this scenario, the apple is falling from a height of 16 feet (d = 16) and we want to find the time it takes for the apple to reach the ground (t). Therefore, we can rewrite the equation as:
16 = 0 * t + (1/2) * 32.2 * t^2
Simplifying further, we have:
16 = 16.1 * t^2
Dividing both sides of the equation by 16.1, we get:
t^2 = 1
Taking the square root of both sides, we find that:
t = ±1
Since time cannot be negative in this context, we discard the negative solution. Therefore, the apple will take approximately 1 second to reach the ground.