An arrow is shot from the top of a platform. The path of the arrow can be modelled by
the relation h = -0.005(t - 26)^2 + 5, where h is the height of the arrow in metres and
t is the time in seconds after the arrow was shot.
a,Find the coordinates of the vertex the parabola
b,how long will it take the arrow to reach its maximum height
c,what is the maximum height
d,what is the height of the building?(calculate h when t=0)
a) To find the coordinates of the vertex of the parabola, we need to convert the equation into vertex form: h = a(t - h)^2 + k, where (h, k) represents the vertex.
Given: h = -0.005(t - 26)^2 + 5
Comparing this with the vertex form, we have a = -0.005, h = 26, and k = 5.
Therefore, the coordinates of the vertex are (26, 5).
b) The time it takes for the arrow to reach its maximum height can be found by determining the horizontal coordinate of the vertex. In this case, the time is given by t = 26.
c) The maximum height can be determined by substituting the time t = 26 into the original equation.
h = -0.005(26 - 26)^2 + 5
= -0.005(0)^2 + 5
= -0.005(0) + 5
= 5
Therefore, the maximum height is 5 meters.
d) To find the height of the building, we need to determine the value of h when t = 0 (at the initial time).
h = -0.005(0 - 26)^2 + 5
= -0.005(-26)^2 + 5
= -0.005(676) + 5
= -3.38 + 5
= 1.62
Therefore, when t = 0, the height of the arrow is approximately 1.62 meters.
a) To find the coordinates of the vertex of the parabola, we need to determine the value of t when the height h is at its maximum. Since the equation for h is in vertex form (h = a(t - h)^2 + k), where (h, k) represents the vertex, we can determine the vertex by comparing it to the given equation.
In this case, the equation h = -0.005(t - 26)^2 + 5 has the vertex in the form (h, k) = (5, 26) because the terms inside the parentheses are (t - 26). Therefore, the coordinates of the vertex of the parabola are (26, 5).
b) To find how long it will take the arrow to reach its maximum height, we need to determine the time value when the height is at its maximum. Since the equation h = -0.005(t - 26)^2 + 5 is a parabolic function, the time taken to reach the maximum height occurs at the vertex. Therefore, the arrow will take 26 seconds to reach its maximum height.
c) To find the maximum height of the arrow, we can use the y-coordinate of the vertex. In this case, at the vertex, h = 5 meters. Therefore, the maximum height of the arrow is 5 meters.
d) To determine the height of the building, we need to calculate h when t = 0. Substituting t = 0 into the equation h = -0.005(t - 26)^2 + 5, we get:
h = -0.005(0 - 26)^2 + 5
h = -0.005(-26)^2 + 5
h = -0.005(676) + 5
h = -3.38 + 5
h = 1.62
Therefore, when t = 0, the height of the building is approximately 1.62 meters.
(a) the equation is already in vertex form, so just read it off.
(b) max height is at the vertex
(c) so, h(26) = ___
(d) h(0) = ____
the only interesting question which cannot just be read directly from the equation is: when did it hit the ground?