Projectile Motion Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A ball is kicked horizontally off a 45 m45 \text{ m} high cliff at 20 m/s20 \text{ m/s}. Using g=10 m/s2g = 10 \text{ m/s}^2: (a) How long until it hits the ground? (b) How far from the base of the cliff does it land?

Solution

  1. 1
    (a) Vertical: h=12gt2h = \frac{1}{2}gt^2. 45=12(10)t245 = \frac{1}{2}(10)t^2, so t2=9t^2 = 9, t=3 st = 3 \text{ s}.
  2. 2
    (b) Horizontal (constant velocity): x=vxt=20×3=60 mx = v_x t = 20 \times 3 = 60 \text{ m}.

Answer

(a)  3 s;(b)  60 m(a)\; 3 \text{ s}; \quad (b)\; 60 \text{ m}
Horizontal and vertical motions are independent. The horizontal velocity stays constant (no horizontal force), while the vertical motion is free fall. The fall time depends only on height, not on horizontal speed.

About Projectile Motion

Two-dimensional motion under gravity alone, where horizontal velocity is constant and vertical motion is uniformly accelerated — producing a parabolic path.

Learn more about Projectile Motion →

More Projectile Motion Examples

Example 1 medium

A ball is launched horizontally at [formula] from a cliff [formula] high. How far from the base of t

Example 2 hard

A projectile is launched at [formula] at [formula] above the horizontal. What is the maximum height

Example 3 medium

A ball is kicked at [formula] at [formula]. What is the range? Use [formula].

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