Suppose you hit a fly ball with an initial upward velocity of 20 feet per second. Which of the following equations would be a realistic model for the height of the ball after t seconds?
which equations...
A. h=-16t^2+20t+300
B. h=-16t^2+20t+30
C. h=-16t^+20t+3
D. h=-16t^+200t+3
The constant it the height at time zero. The coefficient of the t function is the initial velocity.
Answer c seems realistic
h=-16t+200t+3
To determine the realistic model for the height of the ball after t seconds, we need to consider the motion of the ball.
When an object is thrown upwards, it experiences a downward acceleration due to gravity. The equation that describes the height of the ball as a function of time under the influence of gravity is given by:
h(t) = h0 + v0t - 0.5gt^2
Where:
h(t) represents the height of the ball at time t
h0 is the initial height (in this case, 0 since we are measuring from the ground)
v0 is the initial velocity (in this case, 20 ft/s upwards)
g is the acceleration due to gravity (approximately 32.2 ft/s^2, assuming the ball is near the surface of the Earth)
Therefore, the equation that represents the height of the ball after t seconds is:
h(t) = 0 + 20t - 0.5(32.2)t^2
Simplifying this equation, we get:
h(t) = 20t - 16.1t^2
So, the correct equation that represents the realistic model for the height of the ball after t seconds is h(t) = 20t - 16.1t^2.