Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers. To the nearest tenth of a second, how much time would it take the penny to hit the ground? 0.5 seconds 0.6 seconds 0.7 seconds 0.8 seconds
Answers
Answer:
t = 0.6 sec
Step-by-step explanation:
Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers. To the nearest tenth of a second, how much time would it take the penny to hit the ground? 0.5 seconds 0.6 seconds 0.7 seconds 0.8 seconds
0 2
0.1 1.951
0.2 1.804
0.3 1.559
0.4 1.216
0.5 0.775
0.6 0.236
0.7 -0.401
0.8 -1.136
S = ut + (1/2)gt² ( s - distance covered)
u = 0 as it dropped
S = (1/2)gt²
at t = 0
S = 0
=> initial height = 2
Height = Initial height - Distance Covered
=> Height = 2 - S
=> height = 2 - (1/2)gt²
using t= 0.1
=> 1.951 = 2 - (1/2)g(0.1)²
=> -0.049 = - (1/2)g(0.1)²
=> 0.098 = g(0.01)
=> g = 9.8
h = 2 - (1/2)(9.8)t²
=> h = 2 - 4.9t²
h = 0 when hit ground
=> 0 = 2 - 4.9t²
=> t² = 2/4.9
=> t² = 20/49
=> t = 2√5/7
=> t = 2 * 2.236/7
=> t = 0.64 sec
=> t = 0.6 sec
