A baseball is thrown up in the air from a height of 3 feet with an initial velocity of 23 feet per second. When does the baseball hit the ground?
V = Vo + g*Tr = 0.
23 + (-32)Tr = 0,
Tr = 0.72 s. = Rise time.
h = ho + Vo*Tr + 0.5g*Tr^2 = 3 + 23*0.72 + (-16)*0.72^2 = 11.3 Ft. above gnd.
h = 0.5g*Tf^2 = 11.3.
16Tf^2 = 11.3,
Tf = 0.84 s. = Fall time.
Tr + Tf = 0.72 + 0.84 = --------s. = Time to reach gnd.
To find out when the baseball hits the ground, we can use the equation of motion for vertical motion.
The equation for finding the time it takes for an object to hit the ground when thrown up is:
t = (v - u) / g
where:
t is the time taken
v is the final velocity (0 in this case, as it hits the ground)
u is the initial velocity (23 feet per second)
g is the acceleration due to gravity (32 feet per second squared)
Plugging in the values into the equation:
t = (0 - 23) / 32
Simplifying the equation:
t = -23 / 32
Since time cannot be negative, we can disregard the negative sign.
Therefore, the baseball hits the ground after approximately t = 0.719 seconds.
To determine when the baseball hits the ground, we need to find the time it takes for the baseball to reach the ground after it is thrown up.
The motion of the baseball can be described using the equation of motion for vertical motion:
h(t) = h0 + v0t + (1/2)gt^2
Where:
h(t) is the height of the baseball at time t
h0 is the initial height (3 feet in this case)
v0 is the initial velocity (23 feet per second in this case)
g is the acceleration due to gravity (-32.2 feet per second squared)
Since the baseball hits the ground, the height at that time will be zero. So we can set h(t) to zero and solve for t:
0 = 3 + 23t - (1/2)(32.2)t^2
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
In this case:
a = -16.1
b = 23
c = -3
Substituting these values into the quadratic formula, we get:
t = (-23 ± √(23^2 - 4(-16.1)(-3))) / 2(-16.1)
Simplifying this equation will give us two values for t. Since time cannot be negative in this context, we can ignore the negative value. The positive value will be the time it takes for the baseball to hit the ground.
height = -16t^2 + 23t + 3
you want height = 0
so solve the quadratic
-16t^2 + 23t + 3 = 0
or
16t^2 - 23t - 3 = 0
Hint: it does not factor, so use the quadratic formula, reject the negative answer