The Height of a Falling Object Help

Example 1:

An object is dropped from a height of 1600 feet. How long will it take for the object to hit the ground?

Because the object is dropped, the initial velocity, v ₀ , is zero: v ₀ = 0. The object is dropped from a height of 1600 feet, so h ₀ = 1600. The formula h = –16 t ² + v ₀ t + h ₀ becomes h = –16 t ² + 1600. The object hits the ground when h = 0, so h = –16 t ² + 1600 becomes 0 = –16 t ² + 1600.

The object will hit the ground 10 seconds after it is dropped.

Example 2:

A ball is dropped from the top of a four-story building. The building is 48 feet tall. How long will it take for the ball to reach the ground?

Because the object is dropped, the initial velocity, v ₀ , is zero: v ₀ = 0. The object is dropped from a height of 48 feet, so h ₀ = 48. The formula h = –16 t ² + v ₀ t + h ₀ becomes h = –16 t ² + 48. The object hits the ground when h = 0.

The ball will reach the ground in about 1.73 seconds.

An object is dropped from the roof of a 60-foot building. How long must it fall to reach a height of 28 feet?

In the formula h = –16 t ² + v ₀ t + h ₀ , h ₀ is 60 and v ₀ is zero (because the object is dropped). The object reaches a height of 28 feet when h = 28.

The object will reach a height of 28 feet after about 1.41 seconds.

Example 1:

An object is tossed up in the air at the rate of 40 feet per second. How long will it take for the object to hit the ground?

In the formula h = –16 t ² + v ₀ t + h ₀ , v ₀ = 40 and h ₀ = 0.

h = –16 t ² + 40 t

We want to find t when h = 0.

The object will hit the ground after 2.5 seconds.

Example 2:

A projectile is fired upward from the ground at an initial velocity of 60 feet per second. When will the projectile be 44 feet above the ground?

In the formula h = –16 t ² + v ₀ t + h ₀ , v ₀ = 60 and h ₀ = 0.

h = –16 t ² + 60 t

We want to find t when h = 44.

The projectile will be 44 feet off the ground at 1 second (on the way up) and again at 2.75 seconds (on the way down).