A projectile is shot from the ground at an angle of #pi/6 # and a speed of #5 /9 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
The distance is
We apply the equation of motion
to calculate the time to reach the greatest height
To find the distance, we apply the equation of motion
By signing up, you agree to our Terms of Service and Privacy Policy
To find the distance from the starting point when the projectile reaches its maximum height, we can use the following steps:
 Calculate the initial vertical velocity ((V_{i_y})) using the given angle and speed.
 Use the kinematic equation for vertical motion to find the time ((t)) it takes for the projectile to reach its maximum height.
 Use the time obtained in step 2 to find the horizontal distance ((d)) traveled by the projectile using the kinematic equation for horizontal motion.
Given:
 Angle of projection ((\theta)) = (\frac{\pi}{6})
 Initial speed ((V_i)) = (\frac{5}{9}) m/s

(V_{i_y} = V_i \times \sin(\theta)) (V_{i_y} = \frac{5}{9} \times \sin\left(\frac{\pi}{6}\right)) (V_{i_y} = \frac{5}{9} \times \frac{1}{2}) (V_{i_y} = \frac{5}{18}) m/s

Use the equation: (V_f = V_{i_y} + gt) At maximum height, (V_f = 0) (0 = \frac{5}{18}  9.8t) Solve for (t): (t = \frac{5}{18 \times 9.8})

Use the equation: (d = V_{i_x} \times t) (V_{i_x} = V_i \times \cos(\theta)) (V_{i_x} = \frac{5}{9} \times \cos\left(\frac{\pi}{6}\right)) (V_{i_x} = \frac{5}{9} \times \frac{\sqrt{3}}{2}) (V_{i_x} = \frac{5\sqrt{3}}{18}) m/s (d = \frac{5\sqrt{3}}{18} \times \frac{5}{18 \times 9.8})
Calculating (d): (d = \frac{5\sqrt{3}}{18} \times \frac{5}{18 \times 9.8})
Therefore, the distance from the starting point when the projectile reaches its maximum height is approximately 0.063 meters.
By signing up, you agree to our Terms of Service and Privacy Policy
The projectile's distance from the starting point when it reaches its maximum height is ( \frac{25}{27} ) meters.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 A projectile is shot at an angle of #pi/6 # and a velocity of # 2 m/s#. How far away will the projectile land?
 What is the cross product of #[3, 0, 5]# and #[1,2,1] #?
 What is the cross product of #<3,5,8 ># and #<9,3,1>#?
 A projectile is shot at an angle of #pi/4 # and a velocity of # 5 m/s#. How far away will the projectile land?
 A lunch pail is accidentally kicked off a steel beam on a building under construction. Suppose the initial horizontal speed is 1.50 m/s. How far does the lunch pail fall after it travels 3.50 m horizontally?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7