The textbooks say that the maximum range for projectile motion (with no air resistance) is
45 degrees
.
What is maximum range?
The greatest distance a weapon can
fire
without consideration of dispersion.
How do you find the maximum range of a projectile?
Range. The range of the motion is fixed by the condition y=0 . Using this we can rearrange the parabolic motion equation to find the range of the motion:
R=u2⋅sin2θg R = u 2 ⋅ sin 2 θ g
.
What is range of projectile formula?
The range of the projectile is
the displacement in the horizontal direction
. There is no acceleration in this direction since gravity only acts vertically. shows the line of range. Like time of flight and maximum height, the range of the projectile is a function of initial speed.
What is the equation of maximum range?
Range of a Projectile Motion – formula
Equation 2 shows that for a given projectile velocity vo, R is maximum when sin2θo is maximum, i.e. when
θo=45o
.
What is the formula of maximum height?
The maximum height h reached by the projectile is equal to one-half of H, the altitude of this triangle. = H – 1⁄2H so
h = H/2
, which is the desired result.
Why is 45 degrees maximum range?
The sine function reaches its largest output value, 1, with an input angle of 90
degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.
What is the maximum height?
The maximum height of the object is
the highest vertical position along its trajectory
.
What is the relation between maximum height and maximum range?
The initial velocity of the projectile is um/s, H is the maximum height of the projectile and R is its
horizontal range
. In the question, we are asked to find the angle of projection, i.e. θ. To find θ , let us divide the maximum height of the projectile by horizontal range.
What is G in projectile motion?
We can obtain the equations for projectile motion by plugging the appropriate accelerations into the two-dimensional motion equations:
g = 9.8m/s
2
= 32ft/s
2
at the surface of the Earth. The minus sign appearing in the equations indicates that the y-axis must point upwards, or opposite the direction of gravity.
How Does height affect the range of a projectile?
Increasing the launch height increases the downward distance
, giving the horizontal component of the velocity greater time to act upon the projectile and hence increasing the range. “
What is projectile 11th?
A projectile is
any object thrown into space upon which the only acting force is gravity
. … The path followed by a projectile is known as a trajectory. A baseball batted or thrown is an example of the projectile.
How do you find time with maximum height?
Determine the time it takes for the projectile to reach its maximum height. Use the
formula (0 – V) / -32.2 ft/s^2 = T where V
is the initial vertical velocity found in step 2. In this formula, 0 represents the vertical velocity of the projectile at its peak and -32.2 ft/s^2 represents the acceleration due to gravity.
How do you calculate flight time?
To find the time of flight, determine
the time the projectile takes to reach maximum height
. The time of flight is just double the maximum-height time. At maximum height, v
y
= 0. The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.
What is acceleration at maximum height?
At a projectile’s highest point, its
acceleration is zero
.
