A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15 m/s . The ball's height (in meters) after seconds is given by the following.
The height of the ball can be modeled by the equation:
h(t) = -4.9t^2 + 15t + 2
where t is the time in seconds.
The first term (-4.9t^2) represents the effect of gravity (acceleration due to gravity is approximately 9.8 m/s^2 in the downward direction), the second term (15t) represents the initial upward velocity, and the third term (2) represents the initial height.
To find the height of the ball after a certain amount of time, simply plug in the value for t into the equation and solve for h(t). For example, if we want to find the height of the ball after 3 seconds:
h(3) = -4.9(3)^2 + 15(3) + 2
h(3) = -44.1 + 45 + 2
h(3) = 2.9 meters
Therefore, after 3 seconds, the ball is at a height of 2.9 meters.
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15 m/s . The ball's height (in meters) after seconds is given by the following.
h=2+15t-5t
Sorry, there seems to be an error in the expression you provided. The correct expression to model the height of the ball as a function of time would be:
h(t) = -4.9t^2 + 15t + 2
where t is the time in seconds.
This equation takes into account the effect of gravity (represented by the -4.9t^2 term) as well as the initial upward velocity (represented by the 15t term) and the initial height (represented by the +2 constant).
To find the height of the ball at a specific time, simply substitute that time value into the equation and solve for h(t).
To determine the height of the ball after t seconds, we can use the equation of motion for vertical motion under the influence of gravity:
h(t) = h0 + v0t - (1/2)gt^2
Where:
h(t) is the height of the ball at time t
h0 is the initial height
v0 is the initial velocity
g is the acceleration due to gravity.
In this case, the initial height (h0) is 2 meters, the initial velocity (v0) is 15 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Using these values, the equation becomes:
h(t) = 2 + 15t - (1/2)(9.8)t^2
Simplifying further, we have:
h(t) = 2 + 15t - 4.9t^2
Therefore, the height of the ball after t seconds is given by the equation h(t) = 2 + 15t - 4.9t^2.